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THE  NATURE 

AND   THE 

CONSEQUENCES  OF  ANOMALIES 

OF 

REFRACTION 


AN    ESSAY 

ON 

THE    NATURE 

AND   THE 

CONSEQUENCES  OF  ANOMALIES 

OK 

REFRACTION 


BY 

F.  C.  DONDERS,  M.D. 


LATE      PKOFESSOK      OF      PHYSIOLOGY     AND     OPHTHALMOLOGY      IN      THE      UNIVERSITY 
OF    UTRECHT 


(  Translated  under  the  supervision  of  the  Kirschbaum  School  of  Languages 
and  Bureau  of  Translation  of  Philadel/ihia.) 


REVISED   AND    EDITED    BY 


CHARLES  A.  OLIVER,  A.M.,  M.D.  (Univ.  Pa.) 

ONE    OF    THE    ATTENDING    SURGEONS    TO    THE    WILLS'    EYE     HOSPITAL;      ONE    OF    THE 
OPHTHALMIC    SURGEONS    TO    THE    PHILADELPHIA    HOSPITAL,    ETC. 


•JKHitb  portrait  anO  ©tbcr  ITllustrations 


PHILADELPHIA 
P.    BLAKISTON'S    SON    &    CO. 

IOI2     WALNUT    STREET 
1899 


Copyright,  1899,  by  P.  Blakiston's  Son  &  Co. 


PRESS    OF    WM.     F.     FELL    &    CO., 

1220-24  SANS1M  STREET. 

PHILADELPHIA. 


3. 


0  Ki^i,' 


TO 

HERMAN   SNELLEN,  M.D., 

PROFESSOR     OF     OPHTHALMOLOGY     IN     THE     UNIVERSITY 
OF    UTRECHT, 

THIS    ENGLISH    TRANSLATION    OF  THE  WORK    OF   HIS  TEACHER 

AND      PRKUECESSOR      IS     "  IN     TESTIMONY    OF    THE 

WARMEST     FRIENDSHIP     AND      OF 

THE     HIGHEST     ESTEEM" 

De&icateD 

BY    THE    EDITOR. 


EDITOR'S  PREFACE. 


In  his  duties,  the  Editor  has  not  attempted  in 
any  way  to  draw  a  comparison  between  the 
Author's  and  his  own  thoughts  and  beHefs  on 
the  subjects  treated  in  this  volume.  It  has  been 
his  sole  desire  to  give  a  great  man  greater 
honor  and  to  offer  such  a  man's  works  an  in- 
creased amount  of  usefulness.  In  this  spirit, 
and  as  a  result  of  this  thouo-ht,  he  has  oriven 
each  aphorism  exactly  as  it  appeared  in  the 
original  work,  thus  enabling  him  to  show  to 
the  present  ophthalmic  world,  in  spite  of  in- 
numerable controversies,  to  what  slight  extents 
the  fundamental  principles  laid  down  by  the 
talented  Author  in  the  pages  of  his  almost 
unique  brochure  have  suffered  correction,  alter- 
ation, and  conversion  during  the  thirty  pro- 
gressive years  that  have  followed  its  publication. 

Indeed,  it  is  remarkable,  considering  the  many 
ways  in  which  the  finger  of  science  has  in  the 
past  three  decades  since  the  work  was  laid  away 
in  a  comparatively  infrequently  used  language, 
been  guiding  medical  empiricism  by  means  of 
skilled  observation  and  laboratory  research  into 


viii  EDITOR'S  PREFACE. 

the  now  fast  approaching  domain  of  rational 
scientific  medicine,  that  this  man's  work  should 
have  so  much  of  the  real  truth  in  it,  and  that 
his  deductions  should  be  so  certain  of  applica- 
tion to  newly  acquired  facts  that  were  unknown 
at  the  time  he  gave  his  results  to  the  physio- 
logic world.  Here,  in  this  branch  of  medicine 
— in  the  study  of  dioptrics — it  may  be  truly 
said  that  the  proper  application  of  precise  and 
well-grounded  sciences  by  one  who  was  in- 
timately acquainted  with  them  in  their  every 
detail,  to  the  uncertainties  of  new  and  never- 
before-tried  work,  gave  the  Author  answers 
that  were  far  ahead  of  those  that  were  known 
to  the  medical  men  of  his  day. 

To  disturb  such  results,  when  given  in  trust, 
as  it  were,  in  a  posthumous  publication,  would 
be  desecration.  To  give  the  original  conceptions 
of  such  monumental  and  beneficial  labor,  has 
been  a  task  of  veneration  and  love. 

Charles  A.  Oliver. 

Philadelphia,  U.  S.  A.,  1899. 


TABLE  OF  CONTENTS. 


PAGE 

Section       I.  Emmetropia  and  Ametropia,      lo 

Section  II.  Amplitude  of  Accommodation  (Absolute, 
Relative,  and  Binocular)  in  Emmetropia 
and  Ametropia, 19 

Section  III.  Visual  Acuteness  and  Projection  in  Emme- 
tropia and  Ametropia, 30 

Section  IV.  Line  of  Direction,  Center  of  Rotation,  and 
Movements  of  the  Eye  in  Emmetropia 
and  Ametropia 39 

Section     V.  Acuteness    of  Vision    and    Amplitude    of 

Accommodation,  Modified  by  Age,  .    .      44 

Section   VI.  Consequences  of  M  and  of  H, 57 

Section  VII.  Regular  Astigmatism, 69 


ABBREVIATIONS. 


The  following 
E,  . 
M, 
H, 
Hm, 
HI, 
Ht, 
As, 
Pr, 

/,  • 
r,    . 

P,  . 


R, 


A:, 
A„ 
/o, 
/i. 
A. 

Pi. 
P2. 

Ri, 
R2, 

c, 

I,  .' 
/^  ■ 
>, 
<, 

R-P, 
11 
P   R' 


;  abbreviations  are  adopted  in  this  work : 

Emmetropia. 

Myopia. 

Hypermetropia. 

"  ,  Manifest. 

"  ,  Latent. 

,  Total. 
Astigmatism. 
Presbyopia. 

Punctum  proximuni  (nearest  point  of  distinct  vision). 
Punctum  remotissimiitn  (farthest  point  of  distinct  vision). 


.  Distance  from  /  to  k' :     In  M 


diopter. 


Distance  from  r  to  /■''  .•     In  M  =  —  diopter. 

Infinity. 

Absolute  range  of  accommodation  =       diopter. 

Relative  range  of  accommodation. 

Binocular  "       "  <' 

Radius  of  curvature  of  cornea  in  the  visual  line. 

Relative  nearest  point. 

Binocular     "  " 

Relative  farthest  point. 

Binocular     "  " 

Distance  from  p-^  to  k''. 

"  "     r^  "  k^. 

Point  of  convergence  of  visual  lines. 

Anterior  nodal  point. 

Posterior     "       " 

Anterior  focal  point. 

Posterior    "        " 

Distance  of  focal  point  of  a  glass  lens. 

"         "       "        "      "    an  auxiliary  lens  of  the  eye. 
Greater  than. 
Less  than. 
Region  of  accommodation. 

Amplitude  of        " 


A  SUMMARY  OF  THE  NATURE  OF 
ANOMALIES  OF  REFRACTION  AND 
THEIR    CONSEQUENCES. 

In  various  places^  I  have  written  on  tlie 
chanores  that  are  found  in  the  refraction  of  the 
eye,  with  their  symptoms  and  consequences. 
These  writings  contain  a  portion  of  the  results 
of  a  series  of  examinations,  extending  over 
many  thousands  of  eyes,  that  were  commenced 
six  years  ago,  and  have  been  continued  with 
the  collaboration  of  several  of  my  students. 

This  study  gave  the  subject  a  wider  scope 
and,  at  the  same  time,  by  bringing  into  view  the 
connection  between  cause  and  effect,  rendered 
the  knowledge  of  the  subject-matter  more 
thorough  and  its  general  review  much  easier. 
In  fact,  everything  pertaining  to  anomalies  of 
refraction  can,  at  the  present  time,  be  united 
into  an  easily  understood  system. 

Of  that  system,  a  summary  is  hereby  offered 
to  the  reader.  Examination  will  show  that  it 
not  only  contains  what  has  been  previously 
said    on    the    subject,    but   that   it  sums  up  in 

1  See  Bibliography. 
2  9 


lo  ANOMALIES   OF   REFRACTION. 

advance  that  which  will,  in  the  future,  find  a 
more  extended  and  more  comprehensive  con- 
sideration. I  hope,  therefore,  that  it  may  not 
be  unwelcome  as  a  guide  to  some,  as  an  intro- 
d^iction  for  further  study  to  others,  and  as  a 
general  review  to  those  who  may  have  read  and 
heard  of  the  subject  before. 


I.   EMMETROPIA  AND  AMETROPIA. 

I.  Eyes  are  distinguished  into  emmetropic 
and  ametropic  ones.  In  emmetropia,  E  ^  the 
posterior  focal  point,  <f",  of  the  dioptric  system, 
in  a  condition  of  accommodative  rest,  lies  ex- 
actly within  the  retina ;  in  ametropia,  cp"  lies 
either  in  front  of  the  retina  (myopia,  M),  or  is 
situated  behind  it  (hypermetropia,  H). 

II.  E,  therefore,  has  its  most  remote  point  of 
distinct  vision  r  situated  at  co  ,  M  at  a  finite  dis- 
tance in  front  of  the  retina,  and  H  at  a  finite 
distance  behind  the  retina.  The  distance  from 
the  eye  (more  exactly  that  from  the  anterior 
nodal  point  k')  to  r  is  R.  In  M,  R  is  positive, 
in  H  it  is  negative,  and  in  E  it  is  infinite. 

The  nem^est  point  of  distinct  vision  is  p  ;  its 
distance  to  k'  is  P.  The  ran^e  of  accommo- 
dation    may   be    expressed   in    the    number   of 

1  See  List  of  Abbreviations  following  List  of  Contents. 


EMMETROPIA   AND    AMETROPIA.  ii 

diopters  ^  of  the  lens,  which,  during  relaxa- 
tion of  the  muscle  of  accommodation  and 
under  the  conditions  stated  in  Paragraph  IX,  is 
required  to  throw  a  sharp  and  a  clear  image  on 
the  retina.     The  range   of   accommodation  is 

designated  p  —  r  ^^  a* 

III.  The  point  r  is  to  be  determined  by  par- 
allel visual  lines — i.  e.,  by  estimating  the  artificial 
lenses  which  are  required  to  see  luminous 
points  or  fine  streaks  distinctly  at  a  practically 
infinite  distance.  To  determine  the  point  /, 
fine  threads,  or  very  small  luminous  points, 
which  are  to  be  brought  nearer  and  nearer  to 
the  naked  eye  until  their  images  become  indis- 
tinct, are  to  be  used  as  test-objects.  The  de- 
termination should  be  made  during  the  greatest 
amount  of  convergence  of  the  visual  lines  that 
is  obtainable  ;  so  that  consequently,  in  cases  of 
H,  and  frequently  in  those  of  E,  it  becomes 
necessary  to  do  this  by  means  of  convex  lenses, 
the  distances  of  the  points  obtained  being  re- 
duced in  accordance  with  the  method  of  pro- 
cedure. 

IV.  The  measurement  of  the  radius  of  curv- 
ature, /o,  of  two  hundred  corneae  of  eyes  that 
were   partly  emmetropic  and  partly  markedly 

^  Vide  Paragraph  X. 


12  ANOMALIES   OF   REFRACTION. 

ametropic,  by  means  of  Helmholtz's  ophthal- 
mometer, has  shown  that  the  radius  of  corneal 
curvature  in  the  line  of  vision  in  both  conditions 
is  nearly  the  same. 

The  average  condition  found  was  : 

Males.  Females. 

Emmetropia      ^^^=7.785  mm.  ;  7.719  mm.  : 

Myopia              /^=n  7.874     "     ;  7.867    "     : 

Hypermetropia/^,  =  7.96       "     ;  7-767    " 

V.  In  the  myopic  eye,  the  crystalline  lens 
lies  relatively  deeper,  and  therefore  the  dis- 
tance of  the  focal  point  of  the  dioptric  system 
of  such  an  eye  is  correspondingly  somewhat 
greater.  That  the  distance  of  the  focal  point 
of  the  crystalline  lens  itself  should  be  smaller 
has  not  as  yet  been  made  apparent.  In  the 
hypermetropic  eye,  the  crystalline  lens  lies 
closer  to  the  cornea,  and,  consequently,  the 
distance  of  the  focal  point  of  the  dioptric  sys- 
tem of  this  form  of  eye  is  somewhat  shorter. 

VI.  From  Paragraphs  IV  and  V,  the  con- 
clusion follows,  per  exclusionem,  that  the  axis  of 
vision  in  the  myopic  eye  is  the  longer,  and  that 
in  the  hypermetropic  eye  it  is  the  shorter.  This 
has  been  directly  proved,  a,  by  determining  the 
actual  shape  of  the  eyeball  during  life,  which  is 
at  times  made  possible  by  having  the  subject 
direct  the  visual  line  as  far  outward  as  possi- 


EMMETROPIA   AND   AMETROPIA.  13 

ble  ;  b,  by  measurements  made  after  death  in 
numerous  cases  of  M,  and  in  some  cases  of  H  ; 
c,  by  determination  of  the  focal  distance  of  the 
cornea  (estimated  from  its  radius  of  curvature 
p^  of  an  eye  that  had  had  its  crystaUine  lens 
removed  (aphakia),  and  of  that  of  the  artificial 
lens  that  was  necessary  to  cause  the  focal  point 
to  fall  on  the  retina, — and  this  for  eyes  in  which 
the  ametropia,  previous  to  the  extraction  of  the 
crystalline  lens,  could  have  been  determined. 
It  is  possible,  however,  that  H  is  sometimes 
also  caused,  partly,  by  a  greater  focal  distance 
of  a  flatter  crystalline  lens. 

VII.  Through  disease  alone,  the  cornea  be- 
comes the  cause  of  M  ;  sometimes  also  of  H. 
Usually,  however,  its  refraction  is  then  at  the 
same  time  very  irregular.  In  all  the  following 
observations,  these  relatively  rare  cases  of  M 
and  H  are  excluded. 

VIII.  The  individual  differences  of  emme- 
tropic eyes  are  so  slight  that  it  becomes  wholly 
warrantable  in  taking,  after  the  example  of 
Listing,  a  schematic  eye  as  the  basis  for  most 
calculations.  In  M  and  H,  in  which  only  the 
length  of  the  axis  of  vision  deviates  essentially, 
the  same  position  of  the  cardinal  points  may  be 
admitted. 


14  ANOMALIES   OF   REFRACTION. 

IX.  The  degree  of  H  and  M  is  expressed  by 
the  amount  of  refractive  power  of  an  artificial 
lens  that  is  required  for  correction — that  is,  to 
cause  the  focal  point  to  fall  on  the  retina  ;  or, 
in  other  words,  to  allow  the  subject  to  see 
clearly  at  an  infinite  distance.  This  artificial 
lens  is  supposed  to  be  infinitely  thin,  to  stand 
in  the  air,  and  to  coincide  with  k'. 

X.  The  degree  of  refractive  power  of  an 
artificial  lens  is  expressed  by  a  definite  number 

of   diopters,  which  is  equal  to  distance  of  the  focal  point' 

this  distance  beino^  estimated  in  meters.  Arti- 
ficial  lenses  of  plus  five  diopters'  and  of  minus 
four  diopters'  strengths  are  equivalent  to  one- 
fifth  of  a  meter  of  positive  and  to  one-fourth  of 
a  meter  of  negative  distance  of  focal  point. 

M  =  7,00  signifies  a  M,  in  which  an  artificial 
lens  of  seven  diopters'  strength,  and  H  =  3- 50, 
a  H,  in  which  an  artificial  lens  of  three  and  a 
half  diopters'  strength  is  required  for  correction 
under  the  conditions  that  are  noted  in  Para- 
graph IX. 

XI.  About  the  fiftieth  year  of  age,  E  grad- 
ually makes  place  for  H.  Even  at  the  greatest 
age,  however,  the  acquired  H  rarely  reaches 
more  than  one  and  three-quarters  diopters. 
This  is  not  dependent  upon  any  increasing  flat- 


EMMETROPIA   AND    AMETROPIA. 


15 


teninor  of  the  cornea  whose  radius  of  curvature 
rather  sHghtly  decreases  in  aged  persons.  I  have 
found  personally — 


In  79 

men  .... 

.     . 

.    .    .  on  an  average /q 

= 

7 

858 

"  20 

"  under  20  years  of  age   •'   "       "         " 

^ 

7 

932 

'•'51 

"       "      40' 

( ( 

((((        i  i     i  i          a             i  I 

=: 

7 

882 

"  28 

"    over  40 

i  e 

an        an          a             n 

= 

7 

819 

"  II 

"       "     60 

i  i 

an        ( i    a         a             a 

= 

7 

809 

"38 
"    6 

women,  .    .    . 



7 
7 

798 
720 

"  under  20  j 

ears 

ofage  "   "       "         " 

z= 

"  22 

"       "     40 

i  i 

an        i  i     i  i          a             ( < 

= 

7 

799 

"  16 

"    over  40 

" 

4<<(        i  I    i  i          a             ii 

^ 

7 

799 

"    2 

"       "      60 

t  ( 

an        a     ic          a             a 

= 

7 

607 

An  increase  of  the  focal  distance  of  the  crys- 
talline lens,  partly  as  a  consequence  of  flatten- 
ing, and  partly  as  the  result  of  hardening  with 
an  increasing'  refractive  coefficient  of  the  ozUer 
layers,  combined,  in  very  old  age,  with  a  short- 
ening of  the  axis  of  vision,  are  to  be  considered 
as  the  causes  of  acquired  H. 


XII.  M  is  often  hereditary ;  almost  always 
either  in  reality  or  as  disposition  that  is  inborn. 
It  increases  during  the  years  of  development, 
and,  notwithstanding  the  subsequently  increas- 
ing distance  of  the  focal  point  of  the  crystalline 
lens  (XI),  it  remains  progressive  when  it  exists 
in  a  high  degree  (seven  diopters  or  more)  all 
throuorh  life.  As  such,  and  also  in  still  lower 
degrees,  it  is  a  disease  of  the  eye  that  is  based 
upon   an    increasing  morbid    expansion   of  the 


l6  ANOMALIES   OF   REFRACTION. 

ocular  membranes,  coupled  with  ophthalmo- 
scopically  noticeable  atrophy,  and  is  often  asso- 
ciated with  inflammatory  signs  that  are  visible 
in  the  bottom  of  the  eye  ;  a  condition  involving 
various  kinds  of  disturbances  that  are  more  or 
less  necessary, 

XIII.  M  occurs  in  all  orrades  from  zero 
(the  emmetropic  eye)  to  twenty-eight  diopters. 
Grades  of  seven,  nine,  twelve,  and  even  of  four- 
teen diopters  are  not  unusual.  All  distinctions 
between  high  and  low  degrees  are  arbitrary. 
In  zero,  or  emmetropia,  the  axis  of  vision  has 
a  length  of  twenty-two  to  twenty-three  milli- 
meters ;  in  M  of  twenty-eight  diopters  it  has  a 
length  of  about  thirty-one  millimeters.  In  high 
degrees  of  M,  as  proved  by  ophthalmoscopic 
examination,  M  is  present  in  a  higher  degree 
for  direct  vision  (that  is,  in  the  yellow  spot), 
than  it  is  for  indirect  vision  ;  the  expansion  of 
the  ocular  membranes  beinor  the  greatest  at  the 
posterior  pole  of  the  eye, 

XIV.  H  is  usually  hereditary ;  then  it  is 
always  congenital.  It  increases  slightly,  espe- 
cially after  the  fiftieth  year  of  life,  at  which  age, 
in  case  that  E  originally  existed,  H  begins  to 
develop  (compare  Paragraph  XI).  The  lower 
grades  occur  the  most  frequently  ;  grades  of 
six  diopters  are  already  very  rare  ;  while  those 


EMMETROPIA   AND   AMETROPIA.  17 

of  nine  and  twelve  diopters  or  higher  are  only 
found  by  the  way  of  exception. 

XV.  In  the  first  place,  H  is  to  be  separated 
into  inanifest  (Hm)  and  latent  (HI).  Only  in 
Hm  can  the  subject  see  more  clearly  at  a  dis- 
tance with  positive  lenses  ;  in  HI  such  lenses 
are  rejected.  In  HI,  H  is  suppressed  in  conse- 
quence of  an  inherent  exertion  of  accommoda- 
tion which  is  controlled  by  habit  and  can  not  be 
arbitrarily  nullified. 

XVI.  The    QT-reater  -r  is,  the  higher  are  the 

decrees  of  H  that  are  rendered  latent.  Mod- 
erate  degrees  are  also  in  measure  made  mani- 
fest, not  only  permanently  so  in   consequence 

of    a    decrease    of    ^    (with    the    advance    of 

years),  but  also  temporarily,  even  in  youth, 
through  fatigue  following  exertion. 

XVII.  Paralysis  of  accommodation,  tempor- 
arily caused  by  instillations  of  sulphate  of  atro- 
pine (strength,  i  :  1 20 — that  is,  one  part  of  the 
drug  to  one  hundred  and  twenty  parts  of  dis- 
tilled water),  renders  H  entirely  manifest  after 

one  or  two  hours'  time.     If  ^  should  be  very 

great,  Hm  may,  through  the  cycloplegic  action 
of  the  atropine,  rise  from  zero  to  four  and  a 
half  diopters,  and  even    to  six  diopters  ;   from 


i8  ANOMALIES   OF   REFRACTION. 

two  and  a  quarter  to  seven  diopters,  etc.  In  E 
and  in  M,  paralysis  of  accommodation  causes 
the  refraction  to  diminish  barely  one-half  of  a 
diopter  in  amount. 

XVIII.  Hm  is  further  subdivided  into  absolute, 
in  which,  notwithstanding  the  strongest  effort 
of  accommodation,  ^p"  lies  behind  the  retina  ; 
into  relative,  in  which  a  sharply  recognized 
point  p'  is  more  greatly  removed  from  the  eye 
than  the  point  of  convergence  of  the  visual  line 
C  ;  mto  facultative,  in  which,  although  the  con- 
dition may  be  suppressed  by  accommodation, 
yet  weak  positive  lenses  are  not  rejected  for 
distant  vision.  With  the  decrease  of  A,  H, 
which  is  facultative  in  youth,  soon  becomes 
relative,  and  subsequently  absolute. 

XIX.  H  was  observed  and  correctly  charac- 
terized by  Ware  in  1813.  Later,  it  remained 
unmentioned  until  1854,  when  it  was  imperfectly 
described  by  Ruete,  this  being  followed  by  the 
better  explanations  of  Stellwag  von  Carion, 
and  VON  Graefe.  Based  upon  the  results  of 
the  author's  examinations,  it  has  been  shown 
that  low  and  moderate  degrees  of  H  are  very 
common  ;  that  they  prevail  more  frequently 
than  M  ;  that  they  are  sometimes  entirely  lat- 
ent ;  and  that  they  occasionally,  even  in  the 
latent  form,  are   the  underlying  cause  of  two 


EMMETROPIA   AND   AMETROPIA.  19 

important  anomalies  which  thus  far  have  not 
been  well  understood,  convergent  squi7it  and 
asthenopia  or  hebetude  (fatigue  produced  by 
exertion  in  gazing  at  objects  that  are  situated 
close  to  the  eye). 

XX.  The  reason  why  H,  although  generally 
prevailing,  remained  so  long  unrecognized, 
seems  to  be  found  in  the  fact  that  in  very  high 
degrees  of  H  small  objects — for  instance,  type 
of  an  average  size  (partly  because  of  a  more 
rapid  increase  of  the  visual  angle  than  of  the 
circles  of  dispersion  (von  Graefe)  and  partly 
on  account  of  a  oradual  reduction  of  the 
size  of  the  pupil) — can  be  seen  better  near  the 
eye  than  at  some  distance  from  it,  thus  causing 
the  condition  to  be  regarded  as  M  with  weak- 
ness of  sight.  Moreover,  the  minor  degrees 
of  H  are  latent  in  youth,  and  when  exposed  in 
later  life,  are  confounded  with  presbyopia. 


2.  AMPLITUDE  OF  ACCOMMODATION  (ABSO- 
LUTE, RELATIVE,  AND  BINOCULAR)  IN 
EMMETROPIA    AND    AMETROPIA. 

XXI.  The  faculty  of  accommodation  being 
dependent  upon  the  crystalline  lens  growing 
more  convex,  was  assumed  on  eood  orrounds 
by  Young.  This  was  demonstrated  by  Lang- 
ENBECK,  and  especially  by  Cramer,  directly  for 


20  ANOMALIES   OF   REFRACTION. 

the  anterior  surface  of  the  lens  from  the 
changes  of  the  images  of  reflection.  Later, 
these,  as  well  as  those  for  the  posterior  surface 
of  the  lens  (in  a  slighter  degree),  were  proved 
by  Helmholtz,  who  made  further  measure- 
ments and  found  the  results  so  uniform  and 
certain  that  he  concluded  that  the  ordinary 
limits  of  accommodation  could  approximatively 
be  explained  therefrom. 

XXII.  An  alteration  in  the  shape  of  the 
cornea  does  not  take  place  in  accommodation. 
The  theory  of  elongation  of  the  visual  axis 
was  long  ago  refuted  by  Thomas  Young.  It 
appears,  therefore,  that  the  act  of  accommoda- 
tion rests  exclusively  on  changes  that  take 
place  in  the  shape  of  the  crystalline  lens. 
Knapp,  who  in  four  eyes  found  alterations  in 
the  shape  of  the  crystalline  lens,  carefully 
measured  them,  and  proved  that  they  corre- 
sponded tolerably  well  with  the  A  as  deter- 
mined at  the  same  time  according  to  my 
methods  of  visual  tests. 

XXIII.  Formerly,  a  certain  degree  of  ac- 
commodation was  assumed  in  cases  in  which 
there  was  an  absence  of  the  crystalline  lens 
(aphakia).  I  have  shown,  even  in  youthful  sub- 
jects, that  not  the  slightest  trace  of  accommo- 
dation  remains  in   this   condition.        In   efforts 


AMPLITUDE   OF   ACCOMMODATION.  21 

for  accommodation,  connected  with  increased 
convergence,  made  exclusively  by  the  inward 
rotation  of  one  (covered)  eye  with  a  narrowing 
of  the  pupils  of  both  eyes,  a  remote  bright 
point,  sharply  seen  through  the  requisite  lens, 
retained  as  perfectly  its  form  as  it  did  when 
looked  at  with  parallel  visual  lines,  notwith- 
standing that  lenses  of  +0.125  D.  strength 
(obtained  by  a  combination  of  +0.75  D.  with 
—  0.625  D. —  =% — or  inverted)  were  suffi- 
cient to  produce  a  distinct  change  of  form  in 
the  crystalline  lens. 

Herein  lies  a  positive  proof  that  accommoda- 
tion depends  wholly  upon  changes  in  the  shape 
of  the  crystalline  lens. 

XXIV.  A  =  P— R  (compare  Paragraph  III) 
signifies  the  dioptric  power  of  a  positive  lens 
which  the  eye  adds  to  itself  by  the  act  of  accom- 
modation. This  manner  of  expressing  the 
amplitude  of  accommodation  is  in  conformity 
with  the  actual  change  that  may  be  supposed  to 
be  taking  place  by  the  addition  of  an  auxiliary 
positive  meniscus  lens  to  the  anterior  surface  of 
the  crystalline  lens. 

XXV.  This  helping  lens  /'  (/'  denoting  the 
distance  of  the  focal  point)  is,  however,  not  ex- 
actly equal  to  A  =  P — R.  From  the  powers  of 
P  and  R  and  of/'  (computed  from  the  form  of 


22  ANOMALIES   OF   REFRACTION. 

the  crystalline  lens  of  the  same  person,  measured 
during  life,  and  during  accommodation  for  dis- 
tant and  near  vision),  it  has  been  shown  that  in 

the  emmetropic  eye  ^  •  j, 


I  .  I 

9  '  lo 


XXVI.  It  is  further  found  that  /' :  A  slighdy 
differs  in  M  and  H.  If  the  supposition  be  made 
that  the  cardinal  points  have  the  same  situation, 
it  will  be  realized  that  an  equal  change  of  form 
of  the  crystalline  lens  represents  a  slightly 
greater  amplitude  of  accommodation  in  the 
myopic  eye,  and  a  somewhat  smaller  one  in 
the  hypermetropic  eye  than  that  which  is  pres- 
ent in  the  emmetropic  organ.  (In  high  grades 
of  H,  and — as  might  be  expected,  by  reason  of 
the  diseased  stretchino-  of  the  ocular  tunics — 
in  hieh  deofrees  of  M,  much  smaller  values  are 
generally  given  to  both  /'  and  A.) 

XXVII.  A  difference  in  the  value  of  A  in  M 
and  H  of  moderate  degrees  is,  however,  not 
shown  empirically.  It  is  possible  that  the  value 
of  /'  in  myopia  is  in  reality  smaller. 

XXVIII.  When  P  and  R  are  modified  by  the 
employment  of  convex  or  concave  lenses,  they 
are  designated  as  P^  and  R^.  By  the  use  of 
negative  lenses.  P.,  and  R^  become  more  greatly 
removed  than  P  and  R  ;' while  by  the  employ- 
ment of  positive  ones  they  become  less  removed. 


AMPLITUDE   OF   ACCOMMODATION.  23 

Further,  P^ — R^  is  not  equivalent  to  P — R,  but 
becomes  increased  by  the  use  of  concave  lenses, 
and  diminished  by  the  employment  of  convex 
lenses,  these  results  being  the  more  pronounced 
the  further  the  lenses  are  made  to  stand  in  front 
of  the  eye. 

Through  magnifying  lenses  A  is  more  greatly 
diminished.  How  little  remains  during  the  em- 
ployment of  microscopes,  spy-glasses,  and  tele- 
scopes, can  be  readily  determined  when  the 
following  ratios  are  obtained  :     A. 

F',  the  focal  distance  of  the  objective ; 

F",  the  focal  distance  of  the  ocular ; 

X,  the  distance  from  the  objective  to  the  ocular;  and 

y,  the  distance  from  the  ocular  to  /''. 

XXIX.  The  various  grades  of  M  and  of  H  in 
their  relation  to  A  are  represented  graphically 
by  the  table  on  the  following  page. 

The  numbers  i8  to  o  (Fig.  i)  give  the  dis- 
tances of  the  points  of  distinct  vision  that  are 
situated  in  front  of  k\  while  those  below  o,  run- 
ning from  o  to  9,  designate  similar  distances 
that  are  positioned  behind  k' .    Each  of  the  lines 

a,  b,  c,  and  d,  uniting  p  and  r,  shows  the  ampli- 
tudes of  accommodation,  these  being  "propor- 
tional to  the  lengrths  of  the  lines  themselves. 
The  line  a  represents  E,  with  A  ^  9  ;  the  line 

b,  likewise,  shows  E,  with  A  =  1.50  (presby- 
opia) ;  the  line  c  designates  M  =  3,  with  A  = 


24 


ANOMALIES   OF   REFRACTION. 


1 2 — 3  =  9  ;   and   the  line  d,  on  the  contrary, 
exhibits  H  =  3,  with  A  =  3  +  3  =  6. 

XXX.  The  amplitude  of  accommodation  A 
is  the  absolute  one.  For  any  amount  of  posi- 
tive convergence  of  the  visual  lines,  p^  and  rj, 
together  with  Pj  and  Rj,  as  their  distances  to  k', 
are  employed.    The  symbols  A^  =  Pj  —  R^  are 


t8 

IP 

P 

Q 

P 

(; 

3 

P 

^ 

r 

0 

1 

r 

r 

3 

r 

5 

9 

a 

b 

C 

d 

Fig. 

I. 

, 

used  for  the  relative  amplitudes  of  accommoda- 
tion ill  any  given  convergence.  The  farthest  and 
the  nearest  points  seen  simultaneously  by  both 
eyes  are  characterized  as  p^  and  r^ ;  their  dis- 
tances to  k\  as  P2  and  R^  respectively  ;  and  the 
binocular  amplitude  of  accommodation,  as  P2 
— R,  =  A,. 


XXXI.  Fig.  2  represents  the  positions  of  the 


AMPLITUDE   OF   ACCOMMODATION. 


25 


nearest  points,  p„  p^,  and  p,  and  of  the  farthest 
ones  r,  fj,  and  r^  at  differing  divergences,  as 
studied  in  an  emmetropic  eye  of  good  accommo- 
dative power  in  an  intelligent  individual  of  fifteen 
years  of  age  (compare  Paragraph  XXXIV).  The 
numeration  on  the  table  has  the  same  meaning 
as  that  given  above.     The  degree-marks  placed 


1    M 


/ 

/ 

f 

/ 

Y 

^ . 

^ 

^ 

^ 

^ 

/ 

'■^ 

^ 

X 

V 

/ 

/^ 

y 

/ 

/ 

/ 

y 

/ 

/ 

/ 

/ 

/ 

/ 

/ 

y 

ii°.2i'      22°.5o'    34°.32'     46°.38      59°. 20'      7i°.5o' 

Fig.  2. 


below  the  figure,  represent  the  angles  made  at 
the  point  of  convergence  of  the  visual  lines  that 
have  been  calculated  for  a  distance  of  sixty-four 
and  a  half  millimeters  between  the  parallel 
visual  lines  of  the  two  eyes.  On  the  diagonal 
K  K',  the  vertical  lines,  expressing  the  degrees 
of  convergence,  intersect  the  horizontal  ones 
3 


26  ANOMALIES   OF   REFRACTION. 

which  represent  the  distances  in  fractions  of  one 
meter  each  that  correspond  with  these  degrees. 
The  sio-nification  of  the  remaining-  letters  in  the 
figure  can  be  understood  by  reference  to  the 
previous  paragraphs. 

XXXII.  With  the  knowledge  of  the  meaning 
of  the  lines  p„  p^,  and  p,  and  r,  i\,  and  r^,  in 
their  relation  to  the  degrees  of  convergence, 
everything  that  relates  to  accommodation  be- 
comes understandable.  Thus,  from  Fig.  2  the 
following  may  be  inferred: 

E 

A  =  9.75  diopters. 

A3  =  9.25 

Aj — for  ii°2i'  =:  6.00  diopters,  etc. 

XXXIII.  Figure  2,  moreover,  teaches  that, 
as  far  as  p^,  a  portion  of  A  lies  above  and 
another  part  is  situated  below  K  K'.  The  former 
is  the  positive,  and  the  latter  is  the  negative 
portion,  of  the  relative  amplitude  of  accommo- 
dation. Accommodative  action  can  only  be 
continued  for  a  distance  in  which  the  positive 
part  of  A  is  not  too  small  in  comparison  with 
the  negative  portion. 

XXXIV.  To  find  the  lines  j^^j,/^'  and/*  and;-, 
r„  and  i\,  it  becomes  necessary,  in  addition  to 
obtaining  p  and  r,  to  determine  p^^  and  i\  with 


AMPLITUDE   OF   ACCOMMODATION.  27 

various  convex  and  concave  lenses  ;  care  being 
taken  to  take  note  of  every  corresponding  de- 
gree of  convergence.  Further,  by  reduction  of 
pf^  and  ^0,  according  to  the  focal  distances  of  the 
lenses  used,and  their  distances  from  the  eye,  it  is 
obligatory  to  compute  p^  and  r^  in  exact  corre- 
spondence with  the  different  degrees  of  con- 
vergence. The  black  dots  in  figures  2  and  3 
show  the  points  that  have  been  gotten  in  this 
manner. 

XXXV.  For  the  determination  of  these 
measurements,  I  employed  an  optometer,  in 
which  the  lenses,  which  were  laterally  separated 
from  one  another  by  a  distance  that  was  equal 
to  that  of  the  parallel  visual  axes  of  the  two 
eyes,  were  placed  at  0^.5  from  k' .  These  lenses 
were  moved  in  grooves  which  were  so  con- 
structed  as  to  describe  arcs  from  the  turning 
points  of  the  eyes,  in  such  a  way  that  the  dis- 
tances of  the  lenses  to  k'  always  remained  the 
same,  and,  at  every  angle  of  convergence,  the 
visual  axes  coincided  with  the  axes  of  the  lenses 
that  were  employed. 

XXXVI.  The  variation  in  the  forms  of  the 
lines  /j,  p^,  and  /,  and  r,  i\,  and  r^  in  M  and  in 
H  (Fig.  3,  M  and  H)  is  remarkable. 

It  is  apparent  that  with  slight  convergence, 
myopes  can  not  accommodate  so  much  by  far. 


28 


ANOMALIES   OF   REFRACTION. 


and  that  hypermetropes  can  and  must  accom- 
modate more  greatly  than  emmetropes  (com- 
pare Fig.  2).  With  hypermetropes,  only  after 
ciliary  paralysis  has  been  obtained  (vide  Para- 
graph XVII),  can  the  point  r  be  determined  as 
r^, — the  farthest  point  of  total  H,  as  indicated 


tVM. 


1 

T5 


T5 

2 
5T 

1 
5 

2 
T5 


^/ 

/ 

/ 

r 

/ 

/ 

r. 

> 

^ 

/ 

1 

/ 

/ 

/ 

^ 

Et- 



J 

'/ 

J 

/. 

y 

y 

r 

-^ 

Tt 

/ 

h 

P: 

A 

,p 

/ 

'^ 

/ 

r^ 

s^^ 

^ 

y- 

/ 

Vifl 

^. 

y 

^ 

,'' 

^ 

,' 

nt 

rm 

,' 

'' 

n 

i 

Fig.  3. 


in  figure  3.  The  points  r  {i\„^  in  the  figure)  are 
situated  higher  than  would  be  the  case  if  H 
were  not  to  so  o-reat  a  degfree  latent,  beine 
therefore  noted  in  the  figure  as  r,,„  (that  is,  f\  in 
manifest  H).  The  latent  portion,  with  parallel 
visual  lines,  is  shown   by  the  vertical   distance 


AMPLITUDE    OF   ACCOMMODATK3N.  29 

between  r,„  and  r^,  which  Is  here  equal  to  3.50  D., 
while  the  total  hypermetropia,  H  or  Ht,  is  equiv- 
alent to  4.75  D. 


XXXVII.  Dissimilarity  in  the  conformation 
of  the  lines  is  the  consequence  of  practice. 
Myopes  habituate  themselves  to  accommodate 
but  feebly  with  slight  degrees  of  convergence, 
whereas  hypermetropes,  under  similar  circum- 
stances, accommodate  very  forcibly.  By  the 
continual  employment  of  correctional  spectacles, 
the  shapes  of  the  lines  more  nearly  approach 
those  of  emmetropes:  in  a  like  manner,  even  a 
brief  use  of  spectacles  will  have  a  similar  influ- 
ence. 

XXXVIII.  The  form  of  the  lines  /„  /,,  and 
p,  and  r,  1\  and  r^,  in  ametropia,  proves  that 
the  neutralization  of  the  ametropic  condition  by 
concave  or  convex  lenses,  has  not  rendered  the 
eye  similar  to  an  emmetropic  organ. 

XXXIX.  This  makes  manifest  why  each  ame- 
tropic case  should  not  be  at  once  entirely  neu- 
tralized. In  order  to  understand  this  clearly,  r 
in  ametropia  (Fig.  3)  should  be  brought  to  co 
and  the  lines  reduced  in  accordance.  However, 
the  condition  gotten,  does  not  accurately  repre- 
sent that  which  is  really  obtained  by  the  neutrali- 


30  ANOMALIES   OF   REFRACTION. 

zation  of   the  ametropia  (compare    Paragraph 
XXXVIII). 


3.   VISUAL    ACUTENESS    AND    PROJECTION    IN 
EMMETROPIA  AND  AMETROPIA. 

XL.  The  acuteness  of  vision,  V,  of  different 
individuals  is  obtained  and  compared  by  deter- 
mining the  smallest  angle  under  which  they  are 
able  to  recognize  objects  of  known  form  in  an 
illumination  of  average  intensity.  Square  capi- 
tal letters  may  serve  as  objects  (vide  Snellen's 
test-type),  by  which  control  in  reference  to  cer- 
tainty of  recognition  is  vouchsafed  by  the  fact 
that  they  must  be  named.  With  a  normal  eye, 
the  subject  is  able  to  recognize  such  letters 
under  an  angle  of  five  minutes'  opening  (Snel- 
len). Some  subjects  have  the  ability  to  seethe 
test-objects  under  a  smaller  angle. 

Snellen's  test-letters  are  numbered  in  accord- 
ance with  the  distance  D,  at  which  they  can  be 
properly  seen  under  an  angle  of  five  minutes. 
If,  therefore,  the  distance  d,  at  which  the  letters 
can  be  recognized,  is  ascertained,  the  degree  of 

visual  acuteness  will  be  equivalent  to  V  =  j^-  In 
normal  acuity  of  vision,  it  will  be  found  that 
d  ==  D  and  V  =  I. 

XLI.  V  in  M  is  often  imperfect.  In  M>6 
diopters,  it  is  nearly  always   so  unless  the  re- 


VISUAL  ACUTENESS.  31 

fractive  condition  is  congenital  and  the  subject 
is  quite  young.  In  M>7  diopters,  imperfect 
visual  acuity  is  the  ride,  while  in  M>9  diopters, 
it  will  always  be  found  to  be  below  normal. 

XLII.  On  account  of  the  o^reater  distance 
from  k"  to  the  retina  in  M,  retinal  images  for 
equal  angles  under  which  objects  can  be  seen, 
are  larger.  In  opposition,  as  it  were,  the  retina, 
in  consequence  of  stretching,  is  greater  in  ex- 
tent, and,  therefore,  contains  a  fewer  number  of 
percipient  elements  in  any  given  area  of  surface. 
With  a  complete  compensation  of  both  of  these 
factors,  the  projected  retinal  images  would  re- 
tain an  equal  size,  and  V  in  each  case  remain 
the  same.  The  fact  that  V  in  high  degrees  of 
M  is  generally  lessened  in  the  position  of  the 
visual  line,  is — not  considering  diseased  altera- 
tions— explained  by  the  stretching  of  the  ocular 
membranes,  which  has  been  ascertained  ana- 
tomically to  be  relatively  greater  in  the  region 
of  the  yellow  spot. 

XLIII.  In  the  estimation  of  V  with  concave 
lenses  that  neutralize  the  myopic  condition,  it 
will  be  found  that  the  visual  acuity  is  lower  than 
normal.  This  is  so  because  the  second  nodal 
point  k"  (including  the  artificial  lens  in  the 
dioptric  system  of  the  eye)  is  situated  closer  to 
the  retina,  causing  the  retinal  images  to  become 


32  ANOMALIES   OF   REFRACTION. 

smaller.  The  closer  the  correcting  lenses  are 
placed  to  k",  the  more  readily  do  they  neu- 
tralize the  myopia,  the  further  removed  is  k" 
from  the  retinal  plane,  and,  in  consequence,  the 
less  influence  do  they  exert  on  V. 


XLIV.  In  minor  degrees  of  H  that  are  over- 
come by  constant  exercise  of  the  power  of 
accommodation,  V  is  not  infrequently  normal. 
In  addition,  by  reason  of  the  actually  shorter 
distance  of  k"  to  the  retina,  the  retinal  images 
are  not  so  large  as  those  that  are  found  in  an 
emmetropic  eye.  The  retina  of  H,  however, 
offers  a  smaller  surface,  so  that,  notwithstanding 
the  fact  that  the  total  number  of  percipient  ele- 
ments be  equally  great,  they  must  necessarily 
stand  much  closer  to  one  another.  Whether 
such  be  really  the  case,  especially  in  the  region 
of  the  fovea  centralis,  is  well  worthy  of  further 
examination. 

XLV.  In  the  hiofher  o;rades  of  H,  V  is  not 
seldom  found  to  be  imperfect.  In  the  highest 
degrees,  it  is  usually  the  case.  Various  causes 
for  these  results  are  brought  into  play  by  the 
existent  conditions  :  a,  the  retinal  images  are 
smaller  ;  b,  there  often  exists  an  abnormal  sym- 
metry of  the  refracting  surfaces  of  the  eye  ;  and 
c,  in  the  highest  grades  of  H,  the  entire  eye  is 


VISUAL   ACUTENESS.  33 

imperfectly  developed,  die  nerve  taking   share 
in  this  faulty  development. 

XLVI.  When  in  H,  clear  images  are  obtained 
on  the  retinal  plane,  not  by  undue  exertion  of 
the  power  of  accommodation,  but  through  the 
employment  of  bi-convex  lenses  placed  in  front 
of  the  eye,  then  such  retinal  images  (because 
k"  is  moved  forward)  are  probably  as  large  or 
possibly  larger  than  those  that  are  found  in  the 
emmetropic  eye :  consequently,  V  increases. 
In  moderate  degrees,  V  corrected  in  a  similar 
manner,  is  sometimes  >i  ;  in  other  cases,  it  = 
I.  In  hicrh  decrees,  however,  V  remains  often 
<i,  this  generally  resulting  from  the  causes  that 
are  mentioned  in  Paragraph  XLV,  under  d 
and  c. 

XLVII.  In  young  subjects  who  have  been 
successfully  operated  on  for  congenital  cataract, 
and  as  a  result,^have  a  refraction  of  about  H  = 
14.5  to  12  diopters,  H,  when  properly  corrected 
by  a  bi-convex  lens,  often  gives  V>  i .  The  causes 
of  this  are  the  increased  size  of  the  retinal  image, 
and  the  forward  displacement  of  /c"  by  the  sub- 
stitution of  an  artificial  lens  that  is  placed  in 
front  of  the  cornea  for  the  crystalline  lens  which 
was  situated  behind  the  cornea. 

XLVIII.   In  the  correction  of  H,  the  focal  dis- 


34  ANOMALIES   OF   REFRACTION. 

tance  of  the  lens  that  is  used  must  be  as  many 
inches  (milhmeters)  greater  as  the  lens  is  re- 
moved from  the  eye.  As  a  result  of  this,  the 
images  of  the  retina  become  successively  larger 
and  larger  in  size  ;  an  act  that  may  be  compared 
to  that  of  the  working  of  a  Galilean  telescope, 
in  which  the  objective  corresponds  with  the  con- 
vex lens  before  the  eye,  and  the  concave  lens 
of  the  ocular,  in  association  with  the  eye,  may 
be  considered  to  belong  to  a  hypermetropic 
eye.  As  calculation  teaches,  the  magnification 
is  quite  marked.  In  cases  of  H  =  14.5  diop- 
ters, a  lens  of  12  diopters'  strength,  held  at  one 
and  a  half  centimeters'  distance  in  front  of  the 
eye,  produces  a  lineal  magnification  (relatively 
to  an  emmetropic  eye  before  operation)  of  1.322 
times;  while  a  lens  of  2.25  diopters'  strength, 
held  at  ten  centimeters'  distance  in  front  of  the 
eye,  gives  a  magnification  of  more  than  seven 
times  the  true  size. 

In  higher  degrees  of  H  without  aphakia,  simi- 
lar use  may  be  made  of  a  relatively  weak  con- 
vex lens  as  a  Galilean  telescope. 

XLIX.  Lenses  that  magnify  or  minify,  alter 
the  relation  between  the  dimension  of  the 
imaofe  of  the  retina  and  the  movement  of  the 
head  that  is  required  to  survey  an  object  which 
is  situated  in  the  line  of  vision  without  moving 
the  eyeball.      Therefore,   should  the    head  be 


VISUAL  ACUTENESS.  35 

moved  under  such  circumstances,  it  will  appear 
as  if  all  objects  that  are  seen  magnified  are 
advancing  toward  the  eyes,  and  that  all  ob- 
jects that  are  apparently  diminished  in  size 
are  receding  from  the  eyes.  Such,  however, 
is  not  the  case  when  the  eyes  are  moved,  as 
the  disturbed  relationship  is  practically  com- 
pensated for  by  the  incorrect  direction  in  which 
an  object  that  is  seen  obliquely  through  the  lens 
is  supposed  to  lie. 

As  a  rule,  the  various  visual  directions  are 
obtained  in  measure  by  coetaneous  movements 
of  the  head,  and  in  part  by  rotatory  motions  of 
the  eyeball.  In  such  cases,  the  apparent  move- 
ment of  objects  takes  place,  though  only  to  a 
slight  degree,  by  the  employment  of  magnifying 
or  minifying  lenses. 

L,  Magnifying  lenses  have  the  effect  that 
measurements  made  with  them  on  a  surface 
that  is  perpendicular  to  the  visual  line  are  pro- 
jected larger  when  one  eye  is  used  than  with- 
out a  lens ;  whereas,  on  the  contrary,  estima- 
tions of  depth  (differences  of  distance)  made 
under  similar  circumstances  are  projected 
smaller.  Diminishing  lenses  oive  results  that 
are  the  opposite.  The  key  thereto  is  essentially 
this  :  Eqitiform  objects  or  surfaces,  some  angles 
of  which  are  commonly  known  as  right  angles, 
produce,  when  placed  at  similar  distances  and 


36  ANOMALIES   OF   REFRACTION. 

under  equal  inclination,  dissimilar  perspective 
retinal  images  that  are  the  direct  results  of 
differences  of  size.  Consequently,  uniform 
retinal  images,  with  a  difference  in  size,  cause 
them  to  be  projected  as  unlike  objects.  Lenses 
change  merely  the  size,  and  not  the  form,  of 
retinal  images.  Therefore,  their  employment 
gives  rise  to  a  projection  of  other  forms  ;  that  is, 
such,  by  which,  retinal  images  that  are  of  relative 
size,  would  be  produced.  A  study  of  their  con- 
struction teaches  that  these  are  less  deep  the 
larofer  the  retinal  imao-e  becomes,  and  vice 
versa. 

LI.  Likewise,  the  stereoscopic  parallax  for  two 
eyes  is  decreased  by  magnifying  lenses,  and  is 
increased  by  diminishing  ones.  The  explana- 
tion thereof  lies  enclosed  in  this :  that  from 
slightly  remote  objects,  the  angle  under  which  a 
surface  shows  itself  perpendicular  to  the  visual 
axis  is  inversely  proportionate  to  the  distance ; 
while,  on  the  contrary,  the  parallactic  angle  for 
the  two  eyes  is  about  proportionate  to  the 
squares  of  the  distances. 

LII.  In  high  grades  of  myopia  the  retina  is 
stretched.  The  retinal  image  is  therefore  pro- 
jected smaller  than  it  was.  before  the  distention 
took-  place.  With  a  disproportionately  great 
amount  of  stretching  at   the   posterior  pole  of 


VISUAL   ACUTENESS.  37 

the  eye,  an  object  that  is  seen  directly  is  pro- 
iected  smaller  than  it  was  before  the  stretchinof ; 
in  fact,  it  is  projected  smaller  than  it  is  in 
emmetropia  (compare  Paragraph  XLII),  Not- 
withstanding this,  in  fixing  an  object,  its  size  is 
exactly  determined  and  its  boundaries  are  pre- 
cisely indicated  with  the  finger.  In  directing 
the  line  of  vision  successively  upon  the  object's 
diametrically  opposed  boundaries,  the  modified 
connection  between  the  quantity  of  the  neces- 
sary contraction  of  the  muscles  and  the  pro- 
jected size  of  the  images  is  not  indicated  by 
any  apparent  movement  of  the  object. 

Thus,  a  point  of  the  retina  is,  in  consequence 
of  a  slowly  progressive  displacement  by  stretch- 
ing, projected  outwardly  in  a  direction  which 
is  unlike  that  of  the  original.  If  the  line  of 
projection  for  a  selfsame  percipient  element  of 
the  retina  can,  in  spite  of  displacement,  change 
so  as  to  retain  its  connection  with  other  means 
of  perception,  it  is  admissible  to  assume  that 
the  direction  is  not  original,  but  has  been 
brought  into  existence  by  an  association  with 
some  other  means  of  perception. 

« 

LIII.  In  a  similar  manner,  the  projection  of 
the  entire  visual  field,  equally  with  all  its  points, 
can,  under  abnormal  conditions,  be  modified. 
With  any  fixed  state  of  equilibrium  of  the  mus- 
cles of  the  eye,  an  object  that  is  seen  directly, 


38  ANOMALIES   OF   REFRACTION. 

apparently  lies  straight  before  the  eye.  If  the 
position  is  changed  while  the  subject  believes 
that  the  same  equilibrium  has  remained, — in 
paralysis,  for  instance,  or  after  section  of  the 
internal  or  the  external  rectus  muscle,  etc., — he 
will  still  project  that  which  is  seen  centrally, 
directly  in  front  of  his  eyes,  although  the  object 
is  situated  to  one  side ;  the  visual  field  then 
being  improperly  projected.  Studied  in  con- 
nection with  the  other  eye,  it  will  be  found  that 
double  images  are  one  of  the  consequences 
thereof — they  being  homonymous  in  character 
when  the  eye  has  turned  towards  the  nasal 
side,  and  heteronymous  in  type  when  it  has 
deviated  towards  the  temporal  side.  If,  how- 
ever, the  deviated  eye  is  constantly  used  alter- 
nately with  its  fellow, — which  occurs  especially 
in  deviations  toward  the  temporal  side, — it  learns 
to  localize  and  duly  distinguish  its  impressions 
from  those  of  the  other  eye.  The  projection  is 
then  made  with  much  exactness,  and  thus,  the 
situation  of  the  two  objects,  which  have  their 
respective  images  placed  in  the  foveae  centrales 
of  the  yellow  spots  are  shown  as  quite  different. 
Both  yellow  spots  are  thus  no  longer  projected 
towards  the  same  points  in  space.  In  like  man- 
ner, with  such  deviation,  with  or  without  the 
employment  of  weak  prismatic  glasses,  homony- 
mous double  images  are  seen  of  an  object 
whose   retinal   images  fall  to  the  outer  side  of 


VISUAL  ACUTENESS.  39 

the  fovea  centralis  of  the  rio-ht  as  well  as  of  the 
left  eye.  The  reverse  condition  may  appear 
after  a  long-continued  or  a  congenital  deviation 
of  one  eye  to  the  nasal  side. 

LIV.  Herein  lies  the  proof  that,  in  abnormal 
position  of  the  visual  axes,  each  eye  by  itself 
can  learn  to  project  its  field  of  vision  in  the  cor- 
rect direction,  and  that,  therefore,  the  ordinary 
projection  of  the  two  fields  of  vision  upon  each 
other  can  also  be  learned  as  a  consequence  of 
the  subject  seeking  for  corresponding  retinal 
images  for  the  two  keenly  percipient  yellow 
spots.  Accordingly,  through  projection  of  their 
impressions,  with  slight  allowances  to  be  made 
for  one  another,  other  retinal  points  also  acquire 
the  value  of  very  closely  corresponding  points, 
which  signification,  not  being  dependent  on 
any  fundamental  anatomic  condition,  they  may 
also  lose  aeain. 


4.  LINE  OF  DIRECTION,  CENTER  OF  ROTATION, 
AND  MOVEMENTS  OF  THE  EYE  IN  EM- 
METROPIA  AND  IN  AMETROPIA. 

LV.  The  long  axis  {g  a,  Fig.  4)  of  the  corneal 
ellipsoid  cuts  the  cornea  almost  exactly  at  its 
middle  (Helmholtz,  Knapp).  The  same  ap- 
plies to  ametropic  eyes  [g  a,  of  Fig,  5,  showing 
a   myopic   eye,   and  ^  ^  of  Fig.  6,   showing  a 


4° 


ANOMALIES   OF   REFRACTION. 


i 


hypermetropic  one).  The  visual  Hne  //'  is  the 
line  of  direction  which,  extending  through  the 
nodal  point,  unites  the  fixed  point  of  the  object 


Fig.  4. 


i 


^ 

^       W  \i 

\ 

Fig.  5. 

< 

Fig.  6. 


with  its  retinal  image,  which — as  examination 
with  the  ophthalmoscope  has  taught  me — lies  in 
the  fovea  centralis  of  the  yellow  spot. 

The  visual  line  cuts  the  cornea  at  the  nasal 


LINE   OF   DIRECTION,  ETC.  41 

side  and  generally  slightly  above  the  middle 
(Senff,  Helmholtz,  Knapp).  If  the  refracting 
surfaces  are  centered,  as  is  almost  always  the 
case,  the  axis  of  the  cornea  practically  becomes 
at  the  same  time  the  visual  axis,  and  is  crossed 
at  k  by  the  visual  line  under  an  angle  that  is 
shown  hy  I  k  g.  This  angle  is  designated  by 
the  symbol  a. 

LVI.  The  angle  a  differs  in  the  emmetropic 
and  in  the  ametropic  eye.  In  fifteen  emmetropic 
eyes,  we  (Donders  and  Doijer)  found  7°  as  the 
maximum  and  3°5'  as  the  minimum,  with  an  aver- 
age of  5°  .082'  ;  in  twelve  hypermetropic  eyes, 
9°  was  the  maximum,  6°  was  the  minimum,  and 
7°  55'  was  the  average;  in  ten  myopic  eyes, 
the  maximum  equalled  5°  25'  and  the  minimum 
equalled  1°  5'  (that  is,  1°  5'  to  the  temporal 
side  of  the  axis  of  the  cornea,  as  can  be  seen 
in  Figure  5),  with  an  average  of  2°. 

LVII.  The  result  of  the  various  values  of  the 
angle  a  is  that,  with  parallel  visual  lines,  the 
corneal  axes  of  hypermetropes  diverge  more 
than  those  of  emmetropes,  while  those  of  myopes, 
on  the  contrary,  diverge  less,  or  even  converge. 
With  similarly  directed  visual  lines,  therefore, 
myopes  show  an  apparent  convergent  squint, 
while  hypermetropes  exhibit  an  evident  diver- 
gent strabismus. 
4 


42  ANOMALIES   OF   REFRACTION. 

LVIII.  The  cause  of  the  various  values  of 
the  angle  a  is,  as  regards  myopia,  to  be  found 
in  the  stretching  of  all  of  the  ocular  mem- 
branes, mostly  at  the  outer  posterior  portion  of 
the  eyeball,  so  that  the  yellow  spot  is  moved 
towards  the  nasal  side.  In  hypermetropia,  the 
greater  value  of  the  angle  a  is  due  in  measure 
to  the  shorter  distance  between  k"  and  the 
retina,  and  in  part  to  a  congenitally  more  ex- 
ternal situation  of  the  yellow  spot. 

LIX.  The  angle  a  was  obtained  by  determin- 
ing the  angle  formed  between  the  visual  line 
and  the  axis  of  an  ophthalmometer  that  was  re- 
quired to  have  a  flame  placed  in  this  axis,  re- 
flected exactly  in  the  middle  of  the  cornea ; 
the  reflectinor  imaee  beincr  situated  in  the 
middle,  when  each  of  its  double  images  corre- 
sponded precisely  with  the  border  of  the  oppo- 
site double  image. 

LX.  In  the  said  position  of  the  double 
images,  the  designated  angle  of  the  ophthal- 
mometer-plates  simultaneously  indicated  the 
half-breadth  of  the  cornea,  or  rather  its  half- 
chord  ;  the  situation  of  the  turning  point  behind 
this  chord  being  determined  by  calculating  how 
great  the  angles  of  rotation  (equal  on  both 
sides)  must  be  in  order  to  cause  the  extremi- 
ties of  the  chord  to  alternately  come  together 


LINE   OF   DIRECTION. 


43 


with  the  same  point  in  space.  The  probable 
fault  in  this  calculation  amounted  to  less  than 
one  per  cent. 

LXI.  To  the  distance  between  the  corneal 
base  and  the  turning-  point  was  added  two  and 
six-tenths  millimeters  as  the  height  of  the  seg- 
ment of  the  cornea.  In  this  manner  was  found 
column  "b"  of  the  followino-  table: 


•                            Position  of  the  Turning  Point: 

a 

b 

c 

d 

e 

f 

Length  of 

behind 

in  front  of 

Percentage 

behind 

Angle  be- 

the optic 

the 

the  posterior 

proportion. 

the  middle 

tween  the 

axis. 

cornea. 

surface  of  the 
sclerotic. 

of  the 
optic  axis. 

axis  of 
cornea  and 
the  line  of 

vision. 

mm. 

mm. 

mm. 

mm. 

E 

23-53 

13-54  : 

9.99  =  57.32   :   42.48 

1.77 

5°. 082 

M 

25-55 

14.52  : 

11.03  =   56-83   :   43-17 

1-75 

2° 

H 

22. lO 

13.22  : 

8.88  =  59.8     :   40.2 

2.17 

7°-55 

Column  "a  "  was  computed  from  the  ametro- 
pia, in  which  it  was  supposed  that  the  cardinal 
points  corresponded  with  those  of  the  sche- 
matic eye. 

LXII.  The  table  demonstrates  that  the  turn- 
ing point  lies  rather  considerably  behind  the 


44  ANOMALIES   OF   REP"RACTION, 

middle  of  the  visual  axis  with  which  it  was 
formerly  considered  to  almost  meet.  For  the 
hypermetropic  eye,  this  result  is  particularly 
true,  though  perhaps  the  crystalline  lens  in 
such  an  eye  is  less  convex  than  it  is  in  the  em- 
metropic organ,  in  which  the  computed  visual 
axis  (column  "a")  would  be  too  short, and  con- 
sequently, the  turning  point  of  the  eye  would 
lie  relatively  more  anteriorly. 

LXIII.  The  position  found  for  the  turning 
point  of  the  eye  is  advantageous  for  the  move- 
ments of  the  organ.  The  nearer  the  point  of 
rotation  is  situated  to  the  posterior  extremity 
of  the  visual  axis,  the  less  are  the  movements 
restricted  by  the  optic  nerve.  As  a  rule,  the 
larger  eyeball  is  generally  the  cause  of  the  re- 
strained movement  of  the  highly  myopic  eye  ; 
at  least  the  distance  between  the  turning  point 
of  the  eye  and  the  laterally  displaced  optic 
nerve  is  relatively  not  greatly  increased. 


5.  ACUTENESS  OF  VISION  AND  AMPLITUDE  OF 
ACCOMMODATION,  MODIFIED  BY  AGE. 

LXIV.  Figure  7,  herewith  given,  has  been 
copied  from  an  article  by  Dr.  Vroesom  de 
Haan,  entitled  "  Investigations  on  the  Influence 
of  Age  on  Acuteness  of  Vision,"  which  was 
published   at   Utrecht  in    1862.       The   studies 


V  AND    A  AS    MODIFIED    BY    AGE. 


45 


were  made  on  two  hundred  and  eighty-one 
subjects,  one  or  both  of  whose  eyes  were  nor- 
mal, without  any  opacities,  and  free  from  dis- 
turbing astigmatism.  M  >  0.75  diopters,  and 
manifest  H  of  0.5  diopters,  except  in  advanced 
age  when  H  =  1.25  diopters  was  still  allowed, 


Z6M 

24.20 

22:20 

^ 

1 

?0?0 

"~^^ 

K 

m?o 

\ 

/6?n 

\ 

1470 

\ 

h^ 

n?o 

r\ 

lo?n 

V 

8.26 
6-20 

420 

220 

0:20 

40       so 

Fig.  7. 


60 


80       Age. 


were  excluded.     During  the  examination,  care 
was  taken  to  correct  all  ametropia. 


LXV.  In  the  figure,  the  age  is  given  in  the 
abscissas.  The  ordinates  show  V,  which  is  ex- 
pressed by  the  number  of  feet,  d,  at  which  D 
=  XX,  is  recognized.  In  his  investigation,  de 
Haan  required  only  the  recognition  of  the  letters 


46  ANOMALIES   OF    REFRACllON. 

U,  A,  C,  and  L.  As  a  result,  the  equation  that 
he  found  for  V  was  too  large.  An  examination 
has  taught  us  that  on  account  of  this  error,  a 
reduction  of  one-sixth  was  necessary ;  which 
decrease  has  been  introduced  in  the  ficrure. 

LXVI.  The  figure  teaches  that  in  the  emme- 
tropic eye,  up  to  about  the  age  of  twenty-seven 
years,  V  remains  almost  unchanged.  From 
this  age  it  slowly  decreases  until  it  falls  below 
V  =  o.5  in  advanced  life. 

LXVII.  It  further  appears  that  to  the  age  of 
forty-two  years,  V  is,  as  a  rule,  >i.  There 
exists,  however,  quite  pronounced  individual 
differences.  In  cases  in  which  V  =  i,  no  cause 
can  be  properly  assumed  as  to  the  presence  of 
any  anomaly  ;  this  is  the  signification  of  what 
has  been  adopted  by  Snellen  as  V  =  i.  De 
Haan  found  as  his  maximum  that  V  =  1.7. 

LXVIII.  The  studies  were  all  made  under 
adequate  illumination.  A  series  of  personal 
tests,  made  in  each  instance  by  de  Haan,  taught 
him,  however,  that  on  account  of  differences 
in  illumination  under  which  the  examinations 
were  made  on  various  days,  there  appeared 
oscillations  of  V  =  22.5  ;  20,  and  V  =  19.5  : 
20.  These  variations  were,  nevertheless,  fairly 
equally    distributed    over    all    ages.       Conse- 


V  AND   A  AS   MODIFIED   BY    AGE.  47 

quently,  the  line  of  curvature  practically  under- 
went but  slight  change  when  all  of  the  exam- 
inations were  noted  as  being  made  during  equal 
degrees  of  illumination. 


LXIX.  The  cause  of  lessening  acuteness  of 
vision  increasing  with  agfe  must  be  looked  for 
in  the  ocular  media,  as  well  as  in  the  optic 
nerve. 


LXX.  The  remarkable  clearness  with  which 
the  fundus  oculi  of  young  subjects  can  be  seen 
ophthalmoscopically,  confirms  the  belief  that  the 
transparency  and  the  uniformity  of  structure  of 
the  ocular  media  decrease  in  advancing  age. 
The  crystalline  lens  reflects  a  greater  amount 
of  light,  its  tint  grows  more  yellow,  and  by 
oblique  illumination,  the  lines  of  separation  of 
its  sectors  become  more  distinct.  Irregular 
astigmatism  increases.  Monocular  polyopia, 
with  imperfect  accommodation,  in  spite  of  the 
ever-decreasing  pupillary  area,  becomes  more 
pronounced  and  more  disturbing.  The  vitreous 
humor  g^rows  more  turbid  and  becomes  richer 
in  membranes,  corpuscles,  and  filaments,  which, 
as  microscopic  examinations  and  entoptic  studies 
have  taught  me,  are  the  causes  for  so-called 
mouches  volantes.  In  these  changes,  the  cornea 
is  the  least  affected,  particularly,  at  all  events, 
in  its  middle  zone. 


48  ANOMALIES   OF   REFRACTION. 

LXXL  Among  the  most  prominent  altera- 
tions seen  in  the  eye-ground  of  advanced  age, 
are  maculated  thickenings  of  the  membrana 
vitrea  of  the  chorioid — knots,  as  it  were,  that 
penetrate  into  the  retina,  appearing  as  protuber- 
ances which  displace  and  disturb  areas  of  its 
outer  percipient  layer. 

LXXII.  In  high  degrees  of  myopia,  acuteness 
of  vision,  especially,  diminishes  much  more 
quickly  during  advancing  age  than  it  does  in  E. 
In  M  =  9  or  I  2  diopters,  V  at  the  age  of  sixty 
years  is  usually  </^. 

LXXIII.  The  cause  thereof  is,  increasing 
atrophy  of  the  ocular  membranes  through 
stretching ;  this  often  being  coupled  with  a 
chronic,  low-grade  inflammation  combined  with 
a  slight  translucency  of  vitreous  humor.  These 
conditions  may  be  seen  with  the  ophthalmo- 
scope. 

LXXIV.  As  a  rule,  the  amount  of  atrophy  is 
in  direct  relation  with  the  degree  of  M,  though 
in  equivalent  grades  of  M  it  is  found  to  be  pro- 
portionately most  marked  in  older  subjects. 

LXXV.  In  H,  the  decrease  of  V  which  is 
dependent  upon  increase  of  years,  pursues  a 
similar  course  to  that  which  is  seen  in  E. 


V  AND    A  AS    MODIFIED    BY    AGE. 


49 


LXXVI.  The  amplitude  of  accommodation, 
I  :  A,  diminishes  even  somewhat  in  early  life 
(from  the  tenth  year  or  before),  and  decreases 
quite  regularly  so  as  to  about  =  O  at  the  age 
of  sixty  or  seventy  years.     In  addition,  in  the 


M. 


lO    /5    20    25    30    35    40    45   SO    SS    60    65    70    75  80 


\p 

\ 

\ 

\ 

\ 

S, 

\ 

\ 

\ 

\ 

\ 

X 

N, 

\s 

">». 

r 

—1 

^r^: 

p' 

"V 

^ 

Fig.  8. 


emmetropic  eye,  there  is  coetaneously  formed 
a  slight  degree  of  H.  Figure  8,  herewith  given, 
illustrates  this  quite  well,  pp'  is  the  line  of  cur- 
vature of  the  nearest  points,  and  rr'  is  that  of 
the  farthest  points,  expressive  of  the  function- 


50  ANOMALIES   OF    REFRACTION. 

ing  power  of  the  age  (from  ten  to  eighty  years). 
After  the  sixty-fifth  year  of  age,  the  determina- 
tions oi p  become  less  accurate,  this  being  so 
on  account  of  a  lessening  of  V  and  by  reason  of 
the  small  diffusion  circles  that  are  associated 
with  a  narrow  pupil. 

LXXVII.  The  cause  of  the  early  decrease  of 
^  while  the  muscular  mechanism  of  accommo- 
dation is  still  undoubtedly  undisturbed,  is  to  be 
sought  in  the  early  increasing  density  of  the 
crystalline  lens,  whereby  its  capacity  for  change 
of  form  is  decreased.  At  a  greater  age,  there 
is  superadded  to  this  an  actual  diminution  of 
the  anatomical  constituents  of  the  muscular 
mechanism. 

LXXVIII.  The  decrease  of  ^^  in  E  gives 
rise  to  presbyopia,  Pr.  The  point  at  which  Pr 
commences  is  merely  empirical.  Especially 
fine  near-work  can  not  be  done  properly  during 
the  use  of  artificial  light  in  the  evening  when 
P2>2  2  cm.  With  P2>2  2  cm.  I  have  therefore 
proposed  to  let  Pr  commence.  This  happens 
in  cases  of  E  almost  without  exception  between 
the  years  of  forty  and  forty-two.  We  find  the 
degree  of  Pr  to  be  4.5 — p. 

LXXIX.  As  Pr  advances,  the  lines  p^,  p^  and 
p,  and  r,  r^,  and  r^,  in  cases  of  E,  increasingly 


V  AND    A  AS    MODIFIED    BY    AGE. 


51 


assume  the  shape  which  is  primarily  character- 
istic of  H.  Figure  9,  exhibiting  the  accommo- 
dation of  a  forty-three-year-old  subject,  furnishes 
the  proof  thereof.  (Compare  this  with  figure  2 
in  Paragraph  XXXV!.) 

LXXX.    In   M,   the   decrease  of  ^  pursues 


J.  M. 


/ 

/ 

/ 

/ 

/ 

/ 

/ 

/ 

r- 

'/ 

^ 

/ 

-/ 

^ 

r, 

"> 

V 

/ 

r, 

z 

^ 

r- 

22'.50'       J'f'J?'     4$°3d'       SS^ZO'    72'SO 

Fig.  9. 


almost  a  similar  course  to  that  which  is  seen  in 
E.  Solely  in  very  high  degrees,  ^  decreases 
more  quickly  ;  otherwise  the  progress  of  p  is 
altered  by  the  variation  to  which  r,  and  conse- 
quently M,  are  subjected. 

During  the  years  of  development,  M  is,  with- 
out exception,  progressional,  the  rule  being  that 


52 


ANOMALIES   OF   REFRACTION. 


this  is  the  more  pronounced  the  higher  is  the 
grade  of  the  M.  High  degrees  of  M  remain 
progressive  for  long  periods  of  time,  while  the 
highest  grades  of  the  condition  are  continually 
advancing.  • 

LXXXI.  From  the  results  of  a  great  number 
of  examinations  continued  over  a  period  of  many 
years,  and  in  accordance  with  a  comparative 
study  of  the  spectacle  lenses  that  have  been  em- 
ployed for  many  years  past,  and  those  that  are 
still  used,  I  have  projected  the  following  schemas : 


M 


10    15   20   25   30  J5  40   45  50    55  60  65   70   75 


Fig.   io. 


Figure  lo  represents  the  course  of  M  as 
found  in  a  slight  and  almost  stationary  degree 
of  the  condition. 


V  AND   A  AS    MODIFIED    BY    AGE. 


53 


Figure  1 1  illustrates  the  directions  that  are 
assumed  in  a  high-grade,  temporarily  progres- 
sive M. 

Figure  12  shows  the  course  that  is  found  in 
a  very  high,  permanently  progressive  degree, 

LXXXII.  From  this,  it  can  be  seen  that  it  is 


T 

2 
35 

JL 
15 

'ii 

1 
T^ 

2 

^T 

1 

■5 

1 


M. 


/O    15     20    Z5    30   S5    40    4S    50    55    60    65    70    75    80 


-^ 

\ 

\ 

\ 

s 

\ 

N, 

\ 

"v. 

^ 

-^ 

^ 

r' 

V 

/ 

T^ 

Fig.   II. 


an  error  to  suppose  that  M,  as  a  rule,  lessens 
with  an  increase  of  years.  The  cause  of  this 
incorrect  opinion  is  twofold.  In  the  first  place, 
p  actually  recedes  from  the  eye,  and  this  which 
was  considered  as  a  lessening  of  M,  would  only 
take  place  if  r  were  to  withdraw  from  the  organ. 
Secondly,  the  pupil  grows  smaller,  and  conse- 


54 


ANOMALIES   OF   REFRACTION. 


quently,  on  account  of  smaller  circles  of  diffu- 
sion, the  subject  can  often  see  better  at  a  dis- 
tance during  advanced  age,  in  spite  of  a  slightly 
increased  M. 

LXXXIII.   Pr  is  not  excluded  by  minor  grades 


/O      /S     20     2S    30    35     40     45    SO    55     60     65      70     7S    SO 


Fig.    12. 

of  M.  It  is  said  to  be  in  existence  the  moment 
that  P  is  >  22  cm.  In  cases  in  which  M  =  1.5 
diopters  with  A  =  1.5  diopters'  strength,^  is 
situated  at  thirty-three  centimeters  so  that 
Pr  =  4,5  diopters  —  3  diopters  =  1.50  diopters. 


LXXXIV,  The  accompanying  diagram  (fig- 


V  AND    A  AS    MODIFIED    BY    AGE. 


55 


lire  13)  exhibits  approximately  the  course  that 
accommodation,  as  an  attribute  of  age  takes  in 
H.  The  dotted  Hne  r^  r\  gives  the  progress  of 
the  total  H,  while  r,„  r',„  illustrates  that  of  the 
manifest. 

It  is  apparent  that  H,  which  is  entirely  latent 
at    the    outset,   becomes   increasingly   manifest 


Meter 


/O    /5    20    25    30    35    40    45    50  55    60   65    70    75    80 


/{ 


9 
7.5 
6 
45 
3 
1.5 
0 
15 
3 

4.5 
6 

7.5 
[9 


<' 

\ 

s 

\ 

\ 

^ 

N 

N 

s 

N 

V 

Tm. 

^ 

\ 

< 

'rm- 

^ 

^ 

If 

V 

->?, 

'^ 

^ 

^ 

Fig.  13. 


until  by  reason  of  increasing  H,  it  is  finally  ren- 
dered wholly  manifest. 


LXXXV.  Numerous  observations  have  made 
it  probable  that  eyes  which  towards  the  age  of 
full  growth  have  become  emmetropic,  have  had, 
in   earlier  life-time,  a   minor  degree  of  hyper- 


56  ANOMALIES   OF   REFRACTION. 

metropia.  This  is  in  conformance  with  the 
observation  that  M  constantly  augments  during 
the  years  of  development, 

LXXXVI.  Difficulties  with  regard  to  seeing 
at  close  range  arise  sooner  with  H  than  they 
do  with  E.  This,  however,  is  not  Pr,  but  is 
asthenopia.  Pr  is  involved  therewith,  when, 
through  neutralization  of  H  by  the  use  of  an 
artificial  convex  lens,  P  has  become  >^  22  cm. 

LXXXVII.  The  lessening  of  the  amplitude 
of  accommodation,  with  the  increase  of  age, 
takes  place  with  great  regularity.  Favorable 
exceptions  do  not  exist  here.  Well  may  ^ 
lessen  too  rapidly  by  reason  of  illness,  but  out 
of  many  thousands  of  cases  examined,  I  have 
never  seen  any  unusual  continuance.  He  who, 
in  his  forty-eighth  year,  under  definitely  deter- 
mined conditions,  does  not  need  spectacles, 
is,  without  suspecting  it,  more  or  less  myopic 
(sees  distant  objects  more  clearly  through 
slightly  concave  lenses).  An  unusual  degree 
of  V  may  permit  the  possibility  of  a  postpone- 
ment for  one  or  two  years  at  the  most.  He 
who,  though  possessing  V  =  i,  needs  spectacles 
for  reading,  writing,  etc.,  before  his  forty-fifth 
year,  is  generally  more  or  less  hypermetropic 
(sees  clearly  at  a  distance  through  slightly  con- 
vex lenses). 


CONSEQUENCES   OF   M    AND   OF   H.  57 

6.   CONSEQUENCES  OF  M  AND  OF  H. 

LXXXVIII.  The  results  of  a  hiorh  crrade  of 
M  are: 

[a)  Diminution  of  V,  which  especially  becomes 
more  marked  with  increase  of  years  (compare 
Paragraphs  LXXII,  LXXIII,  and  LXXIV)  ; 

[d)  Restrained  movement  of  the  eyeball  with 
absolute  or  relative  insufficiency  (insufficient 
action)  of  the  internal  straight  eye-muscles  ; 

[c)  Divergent  strabismus. 

LXXXIX.  Easily  mobile  emmetropic  eyes 
can  cause  the  visual  lines  to  intersect  on  the 
centre  of  the  plane  of  the  forehead  at  less  than 
5.50  centimeters  from  the  eye,  within  an  angle 
of  80°  or  70°.  If  the  point  of  intersection,  c, 
lies  farther  away  than  seven  centimeters  from 
the  turning  point  of  the  eye,  corresponding  to 
an  angle  of  convergence  of  about  51°,  then, 
in  a  general  way  it  may  be  assumed  that  there 
is  an  insufficiency  of  the  internal  straight  eye- 
muscles. 

XC.  In  M,  even  when  ocular  motion  is  un- 
restrained, relative  insufficiency  is  to  be  sup- 
posed, the  moment  that  it  is  found  that  r^  is 
situated  closer  to  the  eye  than  c.  This  occurs 
the  more  quickly  since  the  position  of  the  line 
of  vision  in  relation  to  the  corneal  axis,  requires 
-     5 


58  ANOMALIES   OF   REFRACTION. 

a  Stronger  convergence  of  the  axis  of  the  cornea 
so  as  to  produce  a  proper  convergence  of  the 
visual  Hues  at  a  definite  distance.  Usually, 
however,  in  addition,  inward  movements  of  eye- 
balls that  are  found  in  high  grades  of  M,  are 
absolutely  restrained. 

XCI.  M  as  well  as  H  are  connected  with 
strabismus.  The  condition  is  present  when  bin- 
ocular vision,  by  reason  of  deviation  of  the 
visual  lines,  is  suspended.  Under  such  cir- 
cumstances, the  visual  lines  do  not  intersect  at 
the  point  on  which  the  attention  is  fixed  ;  and, 
in  fact,  on  but  one  of  the  retinae  has  the  image 
of  this  point  been  placed  in  the  fovea  centralis 
of  the  yellow  spot.  The  other  central  spot  re- 
ceives an  image  from  another  point. 

XCII.  M  is  connected  with  divergoit  strabis- 
mus. The  rule  is,  that  in  high  grades  of  M  this 
variety  of  strabismus  is  relative,  namely,  that 
while  the  visual  lines  are  correctly  directed  for 
seeing  at  a  distance,  i.  e.,  they  are  parallel,  the 
maximum  of  convero-ence  is  insufficient  for 
binocular  near-vision. 

XCIII.  In  relative  diverge7it  strabismus,  con- 
vergence increases,  close  to  its  maximum,  in 
proportion  as  an  object  approaches  the  eye. 
If  the  object  remains  at  that  distance,  then  the 


CONSEQUENCES   OF   M   AND   OF   H.  59 

one  eye  soon  deviates  to  the  temporal  side  ; 
this  taking  place  the  moment  that  it  is  covered 
by  the  hand.  Nevertheless,  if  the  hand  is  taken 
away,  the  outward  deviation  generally  remains, 
showing  that  the  strong  convergence  was  pro- 
duced simply  by  an  effort  to  continue  binocular 
vision. 

XCIV.  The  cause  of  relative  divergent  stra- 
bismus rests  alone  in  the  opposed  convergence. 
The  effort  for  cooperation  of  the  retinae,  that  is 
suspended  in  absolute  strabismus,  can  here  per- 
sist uninterruptedly, 

XCV.  As  one  of  the  results  of  the  highest 
grades  of  M,  the  movement  of  the  eye  to  the 
temporal  side  may  also  be  restrained.  For  near- 
vision,  there  is  a  resultant  relative  divergent 
strabismus  ;  for  distant-vision,  there  is  a  relative 
convergent  strabismus ;  while  for  intervening 
points,  binocular  vision  has  a  restricted  use. 

XCVI.  Divergent  strabismus  is  absolute  when 
binocular  vision  is  not  retained  at  any  distance 
whatever.  In  one  hundred  cases  of  absolute 
divergent  strabismus,  M  was  found  seventy 
times  in  one  or  both  eyes  in  comparatively  high 
degree.  Statistics  thus  prove  a  relationship. 
The  relative  divergent  strabismus,  that  is  char- 


6o  ANOMALIES   OF   REFRACTION. 

acteristic  of  M,  teaches  that  the  connection  is  a 
causal  one. 

XCVII.  If,  therefore,  the  muscles  are  left 
undisturbed,  then, as  a  rule,  strabismus  develops. 
A  correct  direction  of  the  visual  lines  is  only 
gotten  by  an  effort  to  see  similar  objects  directly 
with  both  eyes  ;  that  is,  to  place  the  images  of 
the  same  object  on  both  yellow  spots.  If  one 
eye  is  blind,  it  in  most  instances,  deviates  to  the 
temporal  side. 

XCVIII.  Relative  divergent  strabismus  pro- 
duces dissimilar  images  on  the  two  yellow  spots 
during  near-vision  :  through  this,  the  need  of 
similarity  of  images  in  general  is  diminished. 
A  commencing  deviation,  arising  from  increased 
convero;ence,  reaches  at  once  a  hiph  deo^ree. 
An  exertion  to  converge  is  rather  tedious  be- 
cause it  brings  with  it  an  undue  effort  of  ac- 
commodation, and  therefore  causes  r  to  come 
nearer  to  the  eye.  Inaction  and  decreased 
energy  of  the  internal  rectus  muscles  are  the 
results  of  this.  Feeble  .  resistance  against 
double  images  and  weakened  power  of  the 
internal  straight  muscles  thus  coincide.  When, 
during  this  condition,  the  action  of  these  mus- 
cles is  inadequate  for  seeing  at  a  distance,  then 
an  absolute  divergent  strabismus  is  created. 
This   condition   develops  itself  the  sooner :   a, 


CONSEQUENCES    OF    M    AND   OF    H.  6i 

because  in  the  absence  of  proper  V  at  a  dis- 
tance, double  images  are  but  slightly  disturb- 
ing ;  b,  by  reason  that  when  a  parallelism  of 
the  visual  lines  requires  an  effort  of  the  inter- 
nal recti  muscles,  any  exertion  of  accommoda- 
tion coincides  with  it,  and  reduces  V  for  dis- 
tance ;  c,  because  the  relationship  existing  be- 
tween the  visual  axis  and  the  line  of  vision  in 
myopes  (compare  Paragraph  LVI)  is  not  favor- 
able for  obtaining  a  parallelism  of  the  visual 
lines. 

XCIX.  By  this  means,  a  reason  is  offered 
for  the  origin  of  the  greater  number  of  cases 
of  divergent  strabismus.  Cases  comino^  into 
existence  separately  from  the  influence  of  M, 
are  for  the  greater  part  the  results  of  palsy  or 
blindness  of  one  eye  (compare  Paragraph  XC  VI). 
In  injuries,  contractures  and  complicated  con- 
genital anomalies,  the  cause  is  relatively  seldom 
to  be  found. 

C.  With  E  in  one  eye  and  M  in  the  fellow, 
and  still  more  especially,  with  a  low  grade  of 
M  in  the  one  and  a  high  one  in  the  other, 
divergent  strabismus  is  the  rule.  Various 
forms  can  here  be  differentiated.  In  a  general 
way,  the  interpretation  of  this  rests  in  the  facts 
that,  in  part,  with  the  dissimilarity  in  the  clear- 
ness   and    the    size   of    the    images,    binocular 


62  ANOMALIES   OF   REFRACTION. 

vision  loses  the  greatest  portion  of  its  value; 
and  that  conversely,  the  convergence,  which  is 
already  physically  hindered,  associates  itself 
with  an  exertion  for  accommodation,  and  thus 
diminishes  the  visual  acuity  of  the  slightly 
myopic  eye  for  distance. 

In  this  form  of  strabismus,  especially,  many 
subjects  are  aware  of  the  existent  deviation, 
and  are  capable  of  temporarily  neutralizing  it 
at  will, 

CI.  The  results  of  H  are  asthenopia  and 
convergent  strabismus.  The  former  is  a  quite 
ordinary  symptom,  while  the  latter  is  compara- 
tively seldom  seen. 

CII.  Asthenopia  manifests  itself  as  a  fatigue- 
symptom  that  soon  appears  after  near-vision. 
The  eye  is  not  apparently  diseased,  and  it  is  not 
painful,  even  when  it  is  exerted.  Visual  acuity 
and  the  ocular  movements  are  both  normal. 
Distant  V  is  considered  perfect,  but  reading, 
writing",  etc.,  cause  a  sensation  of  tension  over 
the  eyes.  Objects  become  indistinct.  The  pa- 
tient rubs  the  forehead,  closes  his  eyes,  and 
recommences  his  work,  only  to  sooner  discon- 
tinue than  before.  Rest  relieves  the  ocular 
fatigue,  allowing  a  resumption  of  the  work  for 
a  period  of  time  that  is  commensurate  with  the 
amount  of  rest  that  has  been  taken. 


CONSEQUENCES   OF   M   AND   OF   H.  63 

CIII.  Asthenopia  has  been  confused  with  all 
manner  of  anomalies  and  has  been  especially 
sought  for  in  the  retina.  By  some  it  has  been 
looked  for  in  the  organs  of  accommodation  and 
by  them  has  been  ascribed  to  external  condi- 
tions and  undue  efforts  of  the  eyes.  1  have 
shown  that  asthenopia  is  not  an  accommodative 
anomaly,  but  that  it  is  one  of  refraction ; 
namely,  a  definite  degree  of  H.  Excessive 
action  is  consequently  not  the  cause,  but  the 
essential  inordinate  exertion  presents  difficul- 
ties that  expose  the  primarily  existing  anomaly. 

CIV.  The  production  of  asthenopia  from  H  is 
easy  to  understand.  Visual  acuity  for  distance 
requires  an  exertion  of  the  accommodation  to 
neutralize  H.  Begun  thus  with  a  deficiency, 
the  accommodation  soon  evidences  its  ineffi- 
ciency with  increasing  convergence.  It  is  true, 
the  eye  accustoms  itself  to  accommodate  rela- 
tively very  strongly  with  but  slight  convergence 
(compare  Paragraphs  XXXVI  and  XXXVII), 
but  the  positive  part  of  ^  is  for  moderate  con- 
vergence very  small  in  comparison  with  the 
negative  portion  ;  after  slight  fatigue  it  becomes 
equal  to  O  ;  that  is,  p^  withdraws  to  the  posi- 
tion at  which  fine  work  has  to  be  done.  Should 
the  object  be  removed  to  a  greater  distance, 
this  chanae  eives  but  a  few  moments'  lono-er 
relief,  for  while   at  this   point,  |  is  also  almost 


64  ANOMALIES   OF   REFRACTION. 

entirely  negative,  increasing  fatigue  makes  p^ 
follow  closely  to  the  greater  distance.  For/^, 
all  eyes  are  asthenopic,  especially  emmetropic 
ones. 

CV.  The  stronofer  ^  is,  the  hiofher  in  orrade 
can  H  be  without  producing  asthenopia. 
Whereas  ^  decreases  with  increasing  years, 
asthenopia  manifests  itself  so  much  the  more 
tardily  as  H  is  low  in  degree.  In  H0.75, 
asthenopia  is  not  to  be  found,  or  rather  it 
merges  into  Pr. 

CVI.  The  symptoms  of  asthenopia  and  Pr 
are  unlike:  Presbyopia  entirely  precludes  acute 
vision,  for  instance,  at  twenty  centimeters, 
but  at  a  point  that  is  somewhat  farther  re- 
moved, for  example  at  forty  centimeters,  not 
even  fatigue  may  be  present ;  asthenopia  fre- 
quently permits  vision  at  a  situation  inside  of 
twenty  centimeters,  but  vision  at  a  greater  dis- 
tance, for  example,  forty  centimeters,  is  soon 
followed  by  fatigue. 

CVII.  To  realize  the  difference  between 
asthenopia  and  Pr,  consideration  should  be 
given  to  the  accompanying  distinctive  charac- 
teristics :  I.  The  loss  of  any  fixed  proportion 
of  ^  by  fatigue  has  a  more  greatly  increased 
influence  on   P  and  P^  in  young  hypermetropic 


CONSEQUENCES    OF    M    AND    OF    H.  65 

subjects  than  it  has  in  Pr,  for  the  reason  that  in 
the   latter,  -^  itself  is   much   smaller.      2.  At  a 

greater  distance  than  p^,  the  positive  part  of  ^ 
increases  in  cases  of  Pr  more  quickly  than  it 
does  in  asthenopia.  3.  The  lines  pj,  p^  and  p, 
and  r,  rj  and  r^,  designate  the  change  of  the 
dioptric  system,  and  not  the  exercise  of  the 
muscular  apparatus,  of  which  effort  it  may  be 
taken  for  granted  that,  especially  in  Pr,  each 
addition  produces  a  proportionately  lessened 
change  of  the  crystalline  lens  in  direct  relation 
as  the  bulk  of  the  lens  approaches  its  maxi- 
mum. The  result  of  this  is  that  the  positive 
part  of  ^,  particularly  in  Pr,  expressed  as  a 
muscular  effort,  should  be  much  greater  than 
the  negative  portion. 

CVIII.  The  real  result  of  our  acquaintance- 
ship with  the  origin  of  asthenopia,  is  that  vari- 
ous wearisome  and  troublesome  kinds  of  treat- 
ment, succeeded  by  an  acknowledgment  of 
irremediability,  have  been  abandoned  for  con- 
vex lenses  of  sufficient  streno-ths  to  render  neu- 
tral  at  least  the  manifest  H,  while  each  effort 
to  methodically  accustom  the  eyes  to  increas- 
ingly weaker  lenses  has  been  discontinued. 

CIX.  Convergent    strabismus  is,   ordinarily, 
dependent  on   H.      The  typical  variety  is  de- 


66  ANOMALIES   OF   REFRACTION. 

cidedly  thus  connected.  It  generally  appears 
from  the  fourth  to  the  seventh  years  of  age,  and 
at  times  later,  without  any  complaint  in  regard 
to  double  images,  as  a  periodic  monocular 
squint.  At  first,  most  frequently  noticed  only 
while  gazing  at  near  objects,  followed  later  by 
its  appearance  while  fixing  upon  more  distant 
ones,  it  can  be  restrained  in  its  development  as 
long  as  it  remains  inconstant  by  the  use  of  con- 
vex lenses.  Soon,  however,  it  passes  into  the 
permanent  variety  with  a  constant  deviation 
that  is  generally  confined  to  one  and  the  same 
eye  (strabismus  simplex).  In  this  stage,  there 
is  a  shortening  of  the  internal  recti  muscles, 
additional  motility  inwards,  and  lessened  motion 
outwards  in  both  eyes,  this  being  associated  with 
a  decreased  acuity  of  direct  vision  in  the  devi- 
ated eye  as  well  as  for  indirect  vision  in  the 
visual  field  that  has  remained  common  to  both 
eyes.  This  lowering  of  V  is  gradually  devel- 
oped to  such  a  degree  that  the  deviated  eye, 
during  closure  of  its  fellow,  fails  to  fix  on  an 
object,  but  receives  the  image  on  a  part  of  the 
retina  that  is  situated  to  the  inner  side  of  the 
yellow  spot,  and  thus  actually  distinguishes 
the  object  better  than  by  direct  vision,  i.  e.,  by 
the  receipt  of  the  image  in  the  yellow  spot. 

ex.  The  relationship  between    H   and   con- 
vergent   strabismus    is    quite     manifest :      By 


CONSEQUENCES   OF   M   AND   OF    H.  67 

Stronger  convergence,  H  can  be  more  easily 
overcome,  and  thus  by  an  abandonment  of 
binocular  vision,  the  subject  is  able  to  see  more 
sharply  with  one  eye  and  to  employ  it  more 
constantly  for  near-vision.  Herein  lies  the  rea- 
son why  deviation  at  first  occurs  only  during 
fixation,  and  this  at  an  age  when  keener  obser- 
vation begins.  Further,  while  at  the  time  of 
deviation,  attention  is  directed  upon  a  specific 
object,  yet  it  is  not  odd  that  neither  its  double- 
image  nor  the  object  which  forms  its  image  on 
the  yellow  spot  of  the  deviating  eye,  should 
operate  in  a  disturbing  manner. 

CXI,  However  natural  it  may  be  to  thus  ex- 
plain convergent  strabismus  from  a  causative 
H,  yet  the  condition  is  by  no  means  an  essen- 
tial result  thereof.  The  number  of  hyperme- 
tropes  in  whom  strabismus  is  found  is  in  reality 
relatively  small.  Manifestly,  the  origin  is,  as  a 
rule,  opposed  by  an  inherent  adherence  to 
binocular  vision. 

CXII.  The  conditions  that  promote  the  for- 
mation of  strabismus  in  H  are  of  a  twofold 
character :  a,  those  which  decrease  the  im- 
portance of  binocular  vision  ;  b,  those  which 
make  convergence  easier. 

CXIII.  The  usefulness  of  binocular  vision  is 


68  ANOMALIES   OF   REFRACTION. 

decreased  by  diminished  V  in  one  eye,  fre- 
quently as  a  consequence  of  acquired  corneal 
spots  ;  often  also  inborn,  and  in  this  case,  not 
seldom  dependent  upon  astigmatism. 

CXIV.  Convergence  is  rendered  easier :  i . 
Absolutely,  when  the  eyeballs  offer  but  slight 
resistance  to  movements  to  the  nasal  sides,  and 
the  internal  straight  muscles  possess  an  innate 
preponderance  or  are  readily  controlled  by 
nerve  influence;  2.  relatively,  when  the  line  of 
vision  forms  a  particularly  broad  angle  with  the 
axis  of  the  cornea,  and  thus,  for  vision  at  a  dis- 
tance, a  pronounced  divergence  of  the  axes  of 
the  cornea  is  required.  (Actually,  I  have  found 
the  angle  a  greater  in  convergent  strabismus 
than  in  the  ordinary  examples  of  H  without 
squint.) 

CXV.  In  developed  convergent  strabismus 
in  which  there  is  an  effort  for  near-vision,  the 
deviation  is  very  slight,  in  spite  of  the  fact  that 
exertion  for  convercjence  is  at  this  time  un- 
doubtedly  much  greater.  Consequently,  as 
soon  as  strabismus  is  found  to  be  present,  a 
definite  amount  of  H  does  not  so  easily  pro- 
duce asthenopia.  When  by  tenotomy,  a  proper 
position  has  been  gotten,  convergent  strabis- 
mus often  reappears  from  an  exertion  of  ac- 
commodation.      Under  these    new   conditions, 


REGULAR   ASTIGMATISM.  69 

the  eyeball  moves  (sometimes  arbitrarily)  in- 
wards under  an  impulse  that  as  long  as  the  de- 
viation was  present,  gave  but  slight  movement. 
A  return  of  the  strabismus  is,  in  such  cases 
only  to  be  prevented  by  the  employment  of 
convex  lenses  that  neutralize  the  H. 

CXVI.  Convergent  strabismus  may,  by  way 
of  exception,  depend  upon  a  shortening  of  the 
muscles  caused  by  paralysis  of  the  antagonist, 
by  wounds,  and  by  contractures.  It  may  be 
congenital,  principally  as  a  portion  of  a  com- 
plicated anomaly.  Lastly,  it  may  be  caused 
by  a  subconjunctival  inflammation  which  has 
involved  the  muscle,  this  also  in  measure  ex- 
plaining the  association  between  maculae  of  the 
cornea  and  strabismus. 

The  essential  points  in  tJie  summmy  obtained 
are :  Hypennetropia  gives  rise  to  an  accommo- 
dative asthenopia,  ivhich  can  be  counteracted  by 
an  actively  produced  convergent  strabismus. 

Myopia  leads  to  muscular  asthenopia  which 
yields  to  a  passively  obtained  divergent  stra- 
bismus. 


7.   REGULAR  ASTIGMATISM. 

CXVII.  The  focal  distance  of  the  dioptric 
media  of  the  eye  is,  In  its  various  meridians, 
not   precisely  alike   {regular  astigmatism.  As). 


70  ANOMALIES   OF   REFRACTION. 

If  by  disregarding  the  distance  k'  k"  and  h'  h", 
the  dioptric  system  can  be  imaginarily  reduced 
to  one  refracting  surface,  then  this  practically 
becomes  the  summit  of  an  ellipsoid  with  three 
axes.  The  longest  one  is  the  visual  axis,  while 
the  other  two,  which  are  perpendicular  to  one 
another,  are  situated  in  a  vertical  plane.  The 
directions  of  the  latter  two  are  inconstant. 
Usually,  however,  the  one  deviates  but  slightly 
from  the  horizontal  plane,  while  the  other  de- 
viates but  little  from  the  vertical.  In  four-fifths 
of  the  cases,  the  latter  is  the  shorter. 

The  meridians  extending  through  the  visual 
axis  and  one  of  the  short  axes,  are  known  as 
the  chief  meridians  ;  that  of  maximum  of  curv- 
ature is  expressed  by  ni,  while  that  of  minimum 
of  curvature  is  designated  as  m'. 

CXVIII.  Irregidar  astigmatism  may  be 
traced  to  two  causes  :  a,  the  curvature  of  the 
various  meridians  mutually  differing,  without 
absolutely  corresponding  to  those  of  an  ellip- 
soid with  three  axes ;  b,  monochromatic  homo- 
centric  rays,  refracted  in  one  and  the  same 
meridian,  failinof  to  remain  homocentric. 

CXIX.  Irregular  astigmatism  depends  almost 
always  upon  the  crystalline  lens,  which  is  irreg- 
ular in  every  respect.  This  may  be  inferred 
from   personal    observations.      It    is,  however. 


REGULAR   ASTIGMATISM.  71 

directly  apparent  from  i.  monocular  polyopia; 
2.  the  rays  showing  points  of  light,  and  3. 
the  radiary  lines  of  light  seen  in  the  entoptic 
spectrum  (Listing) — all  of  which  disappear  in 
aphakia  (want  of  the  crystalline  lens).  All  of 
these  appearances  arise  from  the  same  causal 
factor  and  bear  a  direct  relationship  to  irregu- 
lar astigmatism. 

CXX.  In  aphakia,  only  a  definite  amount  of 
regular  astigmatism  remains,  manifesting  itself 
by  a  pure  linear  extension  of  a  point  of  light 
in  two  opposite  directions  (limits  of  Sturm's 
focal  interval),  the  light  at  the  centre  of  the 
focal  interval  being  seen  as  a  round  surface. 
In  nine  cases  of  aphakia  with  V  =  i  or  V>  i, 
m  was  about  seven  times  vertical  in  position 
and  but  once  absolutely  horizontal,  this  being 
proven  by  the  direction  of  the  boundary  lines 
of  the  focal  space.  These  findings  were  proved 
by  measurements  of  the  corneal  radius  in  the 
horizontal  and  the  vertical  meridians. 

CXXI.  The  amount  of  regular  astigmatism. 
As,  is  noted  by  ^,,  /'  being  the  focal  distance  of  a 
cylindrical  lens  which,  added  to  m ',  should 
make  the  focal  distance  in  m '  equal  to  that  of 
m.     I'  is  expressed  in  meters. 

CXXII.  All  eyes  are  astigmatic.    In  ordinary 


72  ANOMALIES   OF   REFRACTION. 

deofrees,  this  can  be  demonstrated  in  a  well- 
acknowledged  manner.  In  very  slight  degrees, 
and  if  there  be  much  associated  irregular  A, 
its  recognition  is  more  difficult.  It,  however, 
can  even  then  be  made  apparent  by  noting  the 
visual  changes  produced  by  rotating  weak 
cylindrical  lenses  (0.25  diopter  cylinder  or  0.50 
diopter  cylinder)  before  the  eye,  for  by  this 
plan,  the  combined  value  of  the  astigmatism  of 
the  lens  and  the  eye  is  obtained  in  certain  posi- 
tions of  the  lens,  while  in  the  opposite  position, 
the  difference  between  the  two  is  grotten. 

CXXIII.  As  <  0.75  diopters  may  be  consid- 
ered as  normal;  As.  0.75  diopters  is  abnor- 
mal, because  V  in  this  condition  is  generally 
lowered  and  the  use  of  cylindrical  lenses  is 
often  of  service.  As  of  6.00  diopters  and  5.00 
diopters  is  not  rare.  I  have  even  seen  As  = 
7,00  diopters. 

CXXIV.  The  asymmetry  just  noted  was  dis- 
covered by  Thomas  Young  in  his  own  eyes  ;  to 
a  very  abnormal  degree  it  was  first  taken  cog- 
nizance of  by  the  astronomer  Airy,  he  finding 
it  in  his  left  eye,  A  few  more  instances  have 
been  met  with  in  Eng-land.  Whewell  crave 
the  condition  the  name  '.astigmatism.'  From 
the  Continent  of  Europe  but  a  single  instance 
has  been  brought  to  our  attention.     This  was 


REGULAR   ASTIGMATISM.  73 

described  by  a  clergyman  living  in  Switzerland 
who  determined  its  presence  in  his  own  eye. 
These  cases  were  improperly  considered  as 
curiosities.  It  has  appeared  to  me  that  out  of 
every  thirty  or  forty  eyes  one  is  affected  with 
an  abnormal  decree  of  regular  astig^matism. 
To  this  type  belong  most  of  the  cases  of  con- 
genitally  defective  vision. 

CXXV,  Just  as  for  normal  astigmatism,  so 
likewise  for  the  abnormal  variety  of  the  defect, 
is  its  seat,  almost  without  exception,  to  be 
looked  ior  pinncipally  in  the  cornea.  This  has 
been  made  apparent  by  comparing  the  degree 
of  As  with  the  variation  in  the  radius  of  corneal 
curvature  in  the  vertical  and  the  horizontal 
meridians,  or  rather,  approximatively  in  ;;/  and 
m' .  Only  when  the  radius  of  curvature  is 
known  in  the  principal  corneal  meridians,  can 
the  positive  and  the  negative  portions  of  the 
crystalline  lens  be  exactly  computed  by  com- 
parison with  the  degree  of  As  and  with  m  and 
m'  of  the  entire  dioptric  system. 

CXXVI.   Recently  I  have  found  a  method  to 

determine  the   principal  corneal  meridians  and 

their  radii  of  curvature.     The  three  lio-hts  whose 

reflectingr    images,    in     imitation    of     Bessel's 

method,  were  employed  by  Helmholtz  for  his 

studies   with    the    ophthalmometer,   are    made 
6 


74  ANOMALIES   OF   REFRACTION. 

movable  in  a  vertical  plane  around  a  point  lying 
in  the  axis  of  the  instrument  which,  during  the 
examination,  is  arranged  so  as  to  coincide  with 
the  cornea.  Without  permitting  any  movement 
of  the  head,  the  radii  of  curvature  in  every 
meridian  may  accordingly  be  measured  by  rotat- 
ing the  lights,  thus  allowinof  the  maximum  and 
the  minimum  meridians  to  be  determined. 


CXXVII.  Abnormal  As.  also  corresponds 
with  the  normal  variety  in  this,  that,  as  a  rule, 
ni  approaches  the  vertical  meridian,  and  m'  the 
horizontal  one.  In  consequence,  it  is  to  be 
considered  as  a  hiQ^her  decree  of  the  same  form 
of  asymmetry  which  is  so  characteristic  of  nor- 
mal eyes. 

CXXVIII.  In  order  to  ascertain  the  degree 
of  As  in  diminished  V.,  we  should  commence 
by  endeavoring  to  determine  the  direction  of 
the  principal  meridians.  This  may  be  accom- 
plished in  two  ways :  i .  From  the  directions  of 
the  lines  under  which  a  point  of  light  is  seen  at 
the  anterior  and  the  posterior  boundary  of  the 
focal  interval.  (These  directions  are  only  inac- 
curately indicated  when  there  is  relatively  much 
associated  As.)  2.  By  rotating  a  cylindrical 
lens  that  is  approximately  correct  in  front  of 
the  eye,  by  which  the  minimum,  and  especially. 


REGULAR   ASTIGMATISM.  75 

the  maximum  degrees  of  V.  can  ordinarily  be 
determined  with  exactness. 

CXXIX.  If  the  direction  of  the  principal 
meridians  is  known,  the  most  practical  way  is 
to  estimate  R  in  each  of  them. 

This  is  accomplished  by  means  of  a  narrow 
slit  (by  preference,  a  transparent  strip  situated 
between  two  blackened  small  glass  plates  that 
are  turned  toward  one  another).  This  is  to  be 
rotated  before  the  eye,  first  in  the  direction  of 
the  one  principal  meridian,  then  in  that  of  the 
other.  In  these  two  meridians,  the  strongest 
convex  lens  or  the  weakest  concave  one  by 
which  the  best  distant  visual  acuity  can  be  got- 
ten, is  to  be  employed. 

CXXX,  By  this  means,  it  is  determined 
whether  E  exists  in  one  of  the  meridians,  and 
to  what  amount  ametropia  is  present  in  one  or 
both  of  the  meridians.  The  degree  of  As  is 
obtained  at  the  same  time  by  the  difference 
of  refraction  in  the  two  meridians. 

CXXXI.  If  E  or  H  be  present  in  one  of  the 
meridians,  it  is  well,  so  as  to  obtain  a  very 
exact  result,  to  previously  paralyze  the  accom- 
modation by  means  of  atropine.  Determina- 
tions of  As  for/  by  accommodation  often  pro- 
duce variable  results,  because  of  the  difference 


76  ANOMALIES   OF   REFRACTION. 

of  accommodative  power  of  both  meridians  in 
two  successive  examinations.  As  a  rule,  how- 
ever, the  same  eye  appears  to  retain  about  the 
same  deo-ree  of  As  durincr  different  accommo- 
dative  conditions. 

CXXXII.  The  astigmatic  lens  contrived  by 
Stokes  to  determine  the  degree  of  astigmatism, 
allows,  after  correction  of  the  astigmatism,  the 
continuance  of  ametropia.  It  therefore  can- 
not ordinarily  be  used  to  advantage  unless 
myopia  in  m  and  7)1 '  (which  is  rarely  so)  be 
present,  in  which  case,  it  may  be  employed  for 
near  reading-tests :  It  neither  teaches  (what 
is  also  necessary  to  know)  the  amount  of 
ametropia  in  each  of  the  principal  meridians. 
In  connection  with  spherical  lenses,  Stokes' 
method  is,  and  ordinarily,  cylindrical  lenses  are 
also,  very  valuable  as  control-tests. 

CXXXIII.  The  method  of  Airy,  too,  is 
merely  of  value  in  myopia  with  astigmatism, 
and  in  such  cases  in  which  there  is  but  slight 
associated  irregular  astigmatism,  gives  alone 
fairly  good  answers.  Modified  for  eyes  that 
are  not  myopic,  the  plan  becomes  less  useful. 

CXXXIV.  As.  may  be  separated  into  sev- 
eral types :    Myopic,   iVm  ;    hypermetropic.  Ah 


REGULAR   ASTIGMATISM.  77 

(which  is  by  far  the  most  frequent)  ;  and  mixed 
astigmatism,  Ahm  or  Amh.  Am  is  said  to  be 
simple,  when  E  exists  in  m ',  and  M  on  the 
other  hand  is  in  ni.  It  is  known  as  coiupoimd 
when  M  exists  in  in '  as  well  as  in  iii,  conse- 
quently giving  M  +  Am.  Likewise,  Ah  is  simple, 
with  E  in  in  and  H  in  in' .  It  is  compound  when 
there  is  H  in  both  m '  and  in,  this  being  ex- 
pressed as  H  +  Ah.  In  mixed  As,  H  is  asso- 
ciated with  m ',  and  M  with  in.  If  M  is  predomi- 
natino-  the  condition  is  known  as  Amh  ;  if  H  is 
predominant,  the  condition  is  designated  by 
Ahm. 

CXXXV.  As.  is  neutralized  (although  not 
with  mathematical  exactness)  by  cylindrical 
lenses.  By  this  correction,  V  is  bettered,  and 
even  at  times,  it  is  doubled  or  quadrupled. 

In  order  to  obtain  R  =  <»  in  in  and  in'  (and 
consequently,  almost  so  in  all  meridians),  are 
required  : 

I.   Simple  cylindrical  lenses  : 

{a)  Positive  ones,  usually  biconvex  in  char- 
acter, with  parallel  axes  of  both  cylinders.  Such 
lenses  are  expressed  by  =-c,  in  which,  the  focal 
distance  L  is  indicated  In  meters.  They  are 
used  for  the  correction  of  simple  Ah. 

{b)  Negative  ones,  ordinarily  biconcave  in 
type  with  parallel  axes.     These  are  designated 


78  ANOMALIES   OF   REFRACTION. 

by  —  -c  and  are   used  for    the    correction    of 
simple  Am. 

2.  Bicylindrical  lenses,  the  one  surface  be- 
ing concave  and  the  other  convex,  with  their 
axes  situated  at  riofht  angles  to  one  another  : 
:^cr— Y^c.  They  are  employed  for  the  correc- 
tion of  Amh  and  Ahm. 

3.  Sphero-cylindrical  lenses,  one  surface  be- 
ing spherical  and  the  other  cylindrical.  When 
both  surfaces  are  convex,  then  they  are  ex- 
pressed  as  -^sc^C;   when  both  are  concave, 

they  are  designated  by  —  ^  s  c  —  ~  C:  compound 
Ah  and  Am, — that  is,  in  H  +  Ah  and  in  M  +  Am. 
When  they  are  employed  In  such  cases  they 
cause  R  to  equal  co.  The  M  and  H  of  these 
compound  refractive  conditions  are  corrected 
by  the  spherical  surfaces,  while  the  remaining 
Ah  and  Am  are  neutralized  respectively  by  the 
convex  and  by  the  concave  cylindrical  surfaces. 
The  adaptation  of  the  lenses  for  cases  in 
which  it  is  desirable  to  bring  R  to  a  determinate 
finite  distance,  is  accomplished  in  accordance 
with  definitely  known  rules,  this  being  mostly 
done  by  alterations  in  the  spherical  surface. 

CXXXVI.  The  symptoms  of  abnormal  As. 
are:  i.  Diminution  of  V  (through  a  peculiar 
deformity  of  the  images  of  the  retina)  ;  some- 
times to  as  much  as  one-fifth  of  normal. 


REGULAR   ASTIGMATISM.  79 

2.  Indifference  to  markedly  dissimilar  spheri- 
cal lenses. 

3.  Broadened  image  of  a  point  of  light  which 
is  elongated  in  two  opposite  directions,  this 
being  obtained  by  holding  different  spherical 
lenses  before  the  eye. 

4.  P  and  R  quite  different  for  lines  in  two 
opposite  directions  that  correspond  with  in  and 
in'. 

5.  Estimation  of  measurements  in  the  said 
directions  likewise  variable,  this  being  in  meas- 
ure due  to  a  difference  in  the  calculated  size  of 
the  retinal  images  by  reason  of  accommodation 
(because  of  the  variability  of  position  oi  k"  in  m 
and  m'\  and  partly  on  account  of  irradiation 
from  unstable  and  inexact  accommodation. 

6.  V  improved  by  gazing  through  a  slit,  es- 
pecially when  the  positions  of  the  slit  are  the 
same  as  the  angles  of  in  or  in' . 

7.  The  appearance  of  two  blue  edges  and  two 
vertically  opposite  red  edges  on  an  illuminated 
square,  when  a  violet  glass  is  held  in  front  of 
the  eye  (this  in  consequence  of  achromatism). 

CXXXVII.  All  these  symptoms  can  be  per- 
sonally observed  by  holding  a  cylindrical  lens 
before  the  eye,  thus  producing  a  fairly  regular 
astigmatism. 

CXXXVIII.  By  adequate  study,  As   can  be 


8o  ANOMALIES   OF   REFRACTION. 

determined  objectively  by  a  recognition  of  the 
difference  in  the  effort  of  accommodation  made, 
in  order  to  sharply  see  ophthalmoscopically  in 
the  perpendicular  image,  vessels  of  the  retina 
that  are  running  off  in  an  opposite  direction. 
In  this  way,  I  am  even  enabled  to  decide  very 
exactly  in  reference  to  the  ametropia  in  two 
opposite  meridians,  and  in  consequence,  the 
degree  of  As.  The  surface  of  the  optic  nerve 
head  appears  elliptically  distorted,  when,  as  a 
rule,  it  is  round  (Knapp).  During  examinations 
with  the  upright  and  the  inverted  image,  it  will 
be  found  that  this  distortion  appears  in  oppo- 
site directions,  this  difference  of  shape  proving, 
as  confirmed  by  further  examination,  the  ex- 
istence of  As  (Schweigger). 

CXXXIX.  As.  may  also  be  recognized  as 
the  result  of  corneal  diseases,  but  in  such  cases, 
it  is  usually  associated  with  much  irregular  As. 
The  same  is  the  case  when,  through  partial 
luxation,  the  crystalline  lens  attains  an  oblique 
position.  If  a  portion  of  the  lens  disappears 
from  the  pupillary  area,  a  high  degree  of  irreg- 
ular As.  becomes  one  of  the  results. 


BIBLIOGRAPHY. 


F.   C.   Donders — Nederlandsch    Tijdschrift  voor  Geneeskiinde,  1858, 
p.  465,  and  1S63,  V. 
"  Ametropie  €71  Iiare gevolgen.     Utrecht,  i860. 

"  Archiv  fur  Ophthalmologie,  iv,  vi,  vii,  und  viii. 

"  Verslageji    en    Mededeelinge7i    van    de  Konmklijke 

Akademie   vatt    Wetenschappe7i,  xi,    159 ;    xiv, 
351 ;  xvi,  etc. 
"  Astigmatisme  e7t  cilindrische  glazen.    Utrecht,  1862. 

(German  edition,  Schweigger,  Berlin  ;  French 
edition,  Dor,  Paris.) 
De    Ruijter — De  Actioiie  At7-op(V  Belladon7i(E  171  iridem.     Inaugural 

Dissertation,  1854.     [Nederhutdsch  Lancet,  iii.) 
McGillavry — Over  de  hoegrootheid  va7i  het  accominodatie-vermoge7i. 

Utrecht,  1858. 
A.  H.  Kuijper — O/idei-zoekiiige/t  betrekkelijk  de  kimstiiiatige  vet-wij- 

ding  van  de7t  oogappel.      Utrecht,  1859. 
H.  de  Brieder — De  sfoor/iisse7t  der  accom7Hodaiie  van  het  oog.    Utrecht, 

1861. 
De  Haas — Geschiedkimdig  o7iderzoek  onitre7it  de  hyper7)ietropie  e7i  hare 

gevolge7i.     Utrecht,  1862. 
F.  C.  Donders  and  D.  Doijer — De  ligging  van  het  draaipunt  va7t 
het  oog  (in  emmetropische  en  ametropicische  oogen),  in  Verslage7i 
en  Mededeeli7ige7i  va/i  de  Ko7ii7iklijke  Akade/iiie  va7i  Wetenschap- 
pe7t,  xiv,  1862,  351. 
Dor — Des  differe7ices  individtiallcs  de  la  refraction  de  rail.     Journal 

de  Phvsiologie  (Brown-Sequard).     Paris,  i860. 
Not  without  connection  with  the  subject,  there  also  appeared: 
H.  Snellen — Letterproeve/i  ter  bepali7ig  der  gezigtsscheipte.     Utrecht, 

1862. 
J.  Vroesom  de  Hann — O7iderzoeki7ige7i   7iaar  den   i/ivloed  va7i  de7i 
Iceftijd  op   de  gesigtsscherpte.      Inaugural   Dissertation,    Utrecht, 
1862. 

81 


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